Restructured notes on combinatorics.

2024-02-19 07:05:13 -07:00 · 2024-02-19 07:05:13 -07:00 · 2a2d8f8195
parent cbca6f018b
commit 2a2d8f8195
12 changed files with 276 additions and 114 deletions
--- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
+++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
@ -89,7 +89,7 @@
    "c/escape-sequences.md": "0d6219ebb51f6f21e026de67603e25b8",
    "c/index.md": "a021c92f19831bdd2bca4cbf813882fe",
    "gawk/index.md": "dd851e023e11c556c0272a0dcb6dd55d",
-    "gawk/variables.md": "a7d95bd458e07b5a329c62366f368c8d",
+    "gawk/variables.md": "73b12bd0d7d6f97b4a7285aaf2c45bfa",
    "index.md": "e48e895feeed7046425bb2ee15419770",
    "journal/2024-01-31.md": "7c7fbfccabc316f9e676826bf8dfe970",
    "journal/2024-02-01.md": "3aa232387d2dc662384976fd116888eb",
@ -101,7 +101,7 @@
    "nix/callPackage.md": "140a02e57cd01d646483e3c21d72243d",
    "nix/index.md": "4efc7fcc4ea22834ba595497e5fb715c",
    "posix/index.md": "97b1b8ecb9a953e855a9acf0ab25b8c8",
-    "posix/signals.md": "2120ddd933fc0d57abb93c33f639afd8",
+    "posix/signals.md": "4fe63c3c9507b2e15c9ad6f3a2b541db",
    "templates/daily.md": "7866014e730e85683155207a02e367d8",
    "posix/regexp.md": "43825a1b9ed0dd7eeb1b6fe35c928bfe",
    "journal/2024-02-04.md": "e2b5678fc53d7284b71ed6820c02b954",
@ -114,7 +114,7 @@
    "_journal/2024-02-02.md": "a3b222daee8a50bce4cbac699efc7180",
    "_journal/2024-02-01.md": "3aa232387d2dc662384976fd116888eb",
    "_journal/2024-01-31.md": "7c7fbfccabc316f9e676826bf8dfe970",
-    "logic/equiv-trans.md": "afcd52fefbbbb8397220194062626a7a",
+    "logic/equiv-trans.md": "4d825c23bf54e8b1e645584d52b2b993",
    "_journal/2024-02-07.md": "8d81cd56a3b33883a7706d32e77b5889",
    "algorithms/loop-invariants.md": "cbefc346842c21a6cce5c5edce451eb2",
    "algorithms/loop-invariant.md": "d883dfc997ee28a7a1e24b995377792b",
@ -149,10 +149,10 @@
    "_journal/2024-02/2024-02-11.md": "afee9f502b61e17de231cf2f824fbb32",
    "encoding/ascii.md": "c01e50f96d0493d94dc4d520c0b6bb71",
    "encoding/index.md": "071cfa6a5152efeda127b684f420d438",
-    "c/strings.md": "e08be6bdc820ec4903480a736448a5d7",
+    "c/strings.md": "2c3b6ecf6cf1815598a7be623983856c",
    "logic/truth-tables.md": "7892ceaa416c9a65acc79ca1e6ff778f",
    "logic/short-circuit.md": "26d300f407f14883022d0ef8dc4f7300",
-    "logic/boolean-algebra.md": "370065481448e60aa8ffa67a437b5482",
+    "logic/boolean-algebra.md": "f9101b2dfdedb73dc13c34c1a70a0010",
    "_journal/2024-02-13.md": "6242ed4fecabf95df6b45d892fee8eb0",
    "_journal/2024-02/2024-02-12.md": "618c0035a69b48227119379236a02f44",
    "binary/shifts.md": "146ee4898faa13b26f00a31024020c2e",
@ -165,10 +165,16 @@
    "algebra/floor-ceiling.md": "456fa31bedb9ec7c2fa1d6f75db81dec",
    "algebra/index.md": "90b842eb694938d87c7c68779a5cacd1",
    "algorithms/binary-search.md": "08cb6dc2dfb204a665d8e8333def20ca",
-    "_journal/2024-02-17.md": "0fad7bf64837646e1018885504d40f41",
+    "_journal/2024-02-17.md": "7c37cb10515ed3d2f5388eaf02a67048",
    "_journal/2024-02/2024-02-16.md": "e701902e369ec53098fc2deed4ec14fd",
    "binary/integer-encoding.md": "a2c8c83a20f1124fd5af0f3c23894284",
-    "combinatorics/index.md": "c5b005bdce7ab01facfd614b00938ef2"
+    "combinatorics/index.md": "f9de9671fdb6068ef2bb5e63051734be",
+    "_journal/2024-02-18.md": "67e36dbbb2cac699d4533b5a2eaeb629",
+    "_journal/2024-02/2024-02-17.md": "7c37cb10515ed3d2f5388eaf02a67048",
+    "combinatorics/multiplicative-principle.md": "aec83fc4bafad4ae17bd3b4e92e068a1",
+    "combinatorics/additive-principle.md": "99320b513f16ef6be62bf766cfbd328d",
+    "_journal/2024-02-19.md": "77ade15d43f3fba69bde96d0e062ec13",
+    "_journal/2024-02/2024-02-18.md": "67e36dbbb2cac699d4533b5a2eaeb629"
  },
  "fields_dict": {
    "Basic": [
--- a/notes/_journal/2024-02-19.md
+++ b/notes/_journal/2024-02-19.md
@ -0,0 +1,11 @@
+---
+title: "2024-02-19"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [ ] Sheet Music (10 min.)
+- [ ] OGS (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [ ] Interview Prep (1 Practice Problem)
+- [ ] Log Work Hours (Max 3 hours)
--- a/notes/_journal/2024-02/2024-02-17.md
+++ b/notes/_journal/2024-02/2024-02-17.md
--- a/notes/_journal/2024-02/2024-02-18.md
+++ b/notes/_journal/2024-02/2024-02-18.md
@ -0,0 +1,23 @@
+---
+title: "2024-02-18"
+---
+
+- [x] Anki Flashcards
+- [x] KoL
+- [ ] Sheet Music (10 min.)
+- [x] OGS (1 Life & Death Problem)
+- [ ] Korean (Read 1 Story)
+- [ ] Interview Prep (1 Practice Problem)
+- [ ] Log Work Hours (Max 3 hours)
+
+* 101weiqi problems (serial numbers)
+	* Q-59934
+	* Q-264298
+	* Q-349700
+	* Q-138042
+	* Q-11151
+	* Q-267485
+	* Q-84172
+	* Q-87250
+	* Q-260737
+	* Q-12517
--- a/notes/c/strings.md
+++ b/notes/c/strings.md
@ -168,7 +168,7 @@ END%%

 %%ANKI
 Cloze
-The {`d` and `i`} format specifer(s) output a(n) {decimal `signed int`}.
+The {`d` and `i`} format specifers output a {decimal `signed int`}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083040-->
@ -184,7 +184,7 @@ END%%

 %%ANKI
 Cloze
-The {`u`} format specifier(s) output a(n) {decimal `unsigned int`}.
+The {`u`} format specifier outputs a {decimal `unsigned int`}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083047-->
@ -201,7 +201,7 @@ END%%

 %%ANKI
 Basic
-Which format specifier(s) were probably used to yield `printf` output `-12`?
+Which format specifiers were probably used to yield `printf` output `-12`?
 Back: `d` or `i`
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
@ -219,7 +219,7 @@ END%%

 %%ANKI
 Cloze
-The {`x`} format specifier(s) output a(n) {lowercase hexadecimal `unsigned int`}.
+The {`x`} format specifier outputs a {lowercase hexadecimal `unsigned int`}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083063-->
@ -227,7 +227,7 @@ END%%

 %%ANKI
 Basic
-Which format specifier(s) were probably used to yield `printf` output `7af`?
+Which format specifier were probably used to yield `printf` output `7af`?
 Back: `x`
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
@ -236,7 +236,7 @@ END%%

 %%ANKI
 Cloze
-The {`X`} format specifier(s) output a(n) {uppercase hexadecimal `unsigned int`}.
+The {`X`} format specifier outputs an {uppercase hexadecimal `unsigned int`}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083074-->
@ -244,7 +244,7 @@ END%%

 %%ANKI
 Basic
-Which format specifier(s) were probably used to yield `printf` output `7AF`?
+Which format specifier were probably used to yield `printf` output `7AF`?
 Back: `X`
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
@ -262,7 +262,7 @@ END%%

 %%ANKI
 Cloze
-The {`o`} format specifier(s) output a(n) {octal `unsigned int`}.
+The {`o`} format specifier outputs an {octal `unsigned int`}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083091-->
@ -279,7 +279,7 @@ END%%

 %%ANKI
 Cloze
-The {`s`} format specifier(s) output a(n) {`NUL`-terminated string}.
+The {`s`} format specifiers outputs a {`NUL`-terminated string}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083100-->
@ -287,7 +287,7 @@ END%%

 %%ANKI
 Basic
-Which format specifier(s) were probably used to yield `printf` output `abc`?
+Which format specifier was probably used to yield `printf` output `abc`?
 Back: `s`
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
@ -296,7 +296,7 @@ END%%

 %%ANKI
 Cloze
-The {`c`} format specifier(s) output a(n) {`char` character}.
+The {`c`} format specifier outputs a {`char` character}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083109-->
@ -304,7 +304,7 @@ END%%

 %%ANKI
 Basic
-Which format specifier(s) were probably used to yield `printf` output `a`?
+Which format specifier was probably used to yield `printf` output `a`?
 Back: `c`
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
@ -313,7 +313,7 @@ END%%

 %%ANKI
 Cloze
-The {`p`} format specifier(s) output a(n) {`void*` address}.
+The {`p`} format specifier outputs a {`void*` address}.
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
 <!--ID: 1707852083117-->
@ -321,7 +321,7 @@ END%%

 %%ANKI
 Basic
-Which format specifier(s) were probably used to yield `printf` output `0b80000000`?
+Which format specifier was probably used to yield `printf` output `0b80000000`?
 Back: `p`
 Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
 Tags: printf
--- a/notes/combinatorics/additive-principle.md
+++ b/notes/combinatorics/additive-principle.md
@ -0,0 +1,56 @@
+---
+title: Additive Principle
+TARGET DECK: Obsidian::STEM
+FILE TAGS: combinatorics set
+tags:
+  - combinatorics
+---
+
+## Overview
+
+The **additive principle** states that two finite and disjoint sets $A$ and $B$ satisfy $$|A \cup B| = |A| + |B|$$
+
+%%ANKI
+Basic
+What does the additive principle state?
+Back: Given finite and disjoint sets $A$ and $B$, $|A \cup B| = |A| + |B|$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738464-->
+END%%
+
+%%ANKI
+Basic
+The additive property applies to sets exhibiting what two properties?
+Back: Finiteness and disjointedness.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738473-->
+END%%
+
+%%ANKI
+Basic
+Why does $|A \cup B| \neq |A| + |B|$ in the general sense?
+Back: Members of $A \cap B$ are counted twice erroneously.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708346613616-->
+END%%
+
+%%ANKI
+Basic
+Which C construct corresponds to the additive property?
+Back: `union`
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+Tags: c
+<!--ID: 1708221293486-->
+END%%
+
+%%ANKI
+Basic
+How do we denote $A$ and $B$ are disjoint using standard set notation?
+Back: $A \cap B = \varnothing$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738491-->
+END%%
+
+## References
+
+* Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
--- a/notes/combinatorics/index.md
+++ b/notes/combinatorics/index.md
@ -1,89 +1,3 @@
 ---
 title: Combinatorics
-TARGET DECK: Obsidian::STEM
-FILE TAGS: combinatorics set
-tags:
-  - combinatorics
-  - set
 ---
-
-## Overview
-
-The **additive principle** states that two finite and disjoint sets $A$ and $B$ satisfy $$|A \cup B| = |A| + |B|$$
-
-The **multiplicative principle** states that two finite sets $A$ and $B$ satisfy $$|A \times B| = |A| \cdot |B|$$
-
-%%ANKI
-Basic
-What does the additive principle state?
-Back: Given finite and disjoint sets $A$ and $B$, $|A \cup B| = |A| + |B|$.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738464-->
-END%%
-
-%%ANKI
-Basic
-What does the multiplicative principle state?
-Back: Given finite sets $A$ and $B$, $|A \times B| = |A| \cdot |B|$.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738469-->
-END%%
-
-%%ANKI
-Basic
-The additive property applies to sets exhibiting what two properties?
-Back: Finiteness and disjointedness.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738473-->
-END%%
-
-%%ANKI
-Basic
-The multiplicative property applies to sets exhibiting what property?
-Back: Finiteness.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738477-->
-END%%
-
-%%ANKI
-Cloze
-The additive principle is to {$\cup$} whereas the multiplicative principle is to {$\times$}.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738480-->
-END%%
-
-%%ANKI
-Basic
-If $A$ is finite, how is $A \times B$ rewritten as $|A|$ disjoint sets?
-Back: Given $A = \{a_1, \ldots, a_n\}$, $(\{a_1\} \times B) \cup \cdots \cup (\{a_n\} \times B)$.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738483-->
-END%%
-
-%%ANKI
-Basic
-If $B$ is finite, how is $A \times B$ rewritten as $|B|$ disjoint sets?
-Back: Given $B = \{b_1, \ldots, b_n\}$, $(A \times \{b_1\}) \cup \cdots \cup (A \times \{b_n\})$.
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738487-->
-END%%
-
-%%ANKI
-Basic
-How do we denote $A$ and $B$ are disjoint using standard set notation?
-Back: $A \cap B = \varnothing$
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738491-->
-END%%
-
-%%ANKI
-Basic
-How is the cartesian product $A \times B$ defined?
-Back: $A \times B = \{\langle x, y \rangle : x \in A \land y \in B\}$
-Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
-<!--ID: 1708217738494-->
-END%%
-
-## References
-
-* Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
--- a/notes/combinatorics/multiplicative-principle.md
+++ b/notes/combinatorics/multiplicative-principle.md
@ -0,0 +1,120 @@
+---
+title: Combinatorics
+TARGET DECK: Obsidian::STEM
+FILE TAGS: combinatorics set
+tags:
+  - combinatorics
+  - set
+---
+
+## Overview
+
+The **multiplicative principle** states that two finite sets $A$ and $B$ satisfy $$|A \times B| = |A| \cdot |B|$$
+
+%%ANKI
+Basic
+What does the multiplicative principle state?
+Back: Given finite sets $A$ and $B$, $|A \times B| = |A| \cdot |B|$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738469-->
+END%%
+
+%%ANKI
+Basic
+The multiplicative property applies to sets exhibiting what property?
+Back: Finiteness.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738477-->
+END%%
+
+%%ANKI
+Cloze
+{`union`} is to the additive property whereas {`struct`} is to the multiplicative property.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+Tags: c
+<!--ID: 1708221293483-->
+END%%
+
+%%ANKI
+Basic
+Which C construct corresponds to the multiplicative property?
+Back: `struct`
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+Tags: c
+<!--ID: 1708221293489-->
+END%%
+
+%%ANKI
+Cloze
+The additive principle is to {$\cup$} whereas the multiplicative principle is to {$\times$}.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738480-->
+END%%
+
+%%ANKI
+Basic
+If $A$ is finite, how is $A \times B$ rewritten as $|A|$ disjoint sets?
+Back: Given $A = \{a_1, \ldots, a_n\}$, $(\{a_1\} \times B) \cup \cdots \cup (\{a_n\} \times B)$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738483-->
+END%%
+
+%%ANKI
+Basic
+If $B$ is finite, how is $A \times B$ rewritten as $|B|$ disjoint sets?
+Back: Given $B = \{b_1, \ldots, b_n\}$, $(A \times \{b_1\}) \cup \cdots \cup (A \times \{b_n\})$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738487-->
+END%%
+
+%%ANKI
+Basic
+How is the cartesian product $A \times B$ defined?
+Back: $A \times B = \{\langle x, y \rangle : x \in A \land y \in B\}$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708217738494-->
+END%%
+
+%%ANKI
+Basic
+How many functions exist between $\{1, 2, 3, 4, 5\}$ and $\{a, b, c, d\}$?
+Back: $4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = 4^5$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708221293492-->
+END%%
+
+%%ANKI
+Basic
+How many functions exist between finite sets $A$ and $B$?
+Back: $|B|^{|A|}$
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708221293496-->
+END%%
+
+%%ANKI
+Basic
+What combinatorial concept explains the number of functions between two finite sets?
+Back: The multiplicative principle.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708351482412-->
+END%%
+
+%%ANKI
+Basic
+How is the "count of three letter license plates" reimagined as a count of functions?
+Back: As the number of functions from $\{1, 2, 3\}$ to $\{A, B, \ldots, Z\}$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708221293499-->
+END%%
+
+%%ANKI
+Basic
+How is the "maximum unsigned $w$-bit number" reimagined as a count of functions?
+Back: As one less than the number of functions from $\{1, 2, \ldots, w\}$ to $\{0, 1\}$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1708221293502-->
+END%%
+
+## References
+
+* Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
--- a/notes/gawk/variables.md
+++ b/notes/gawk/variables.md
@ -207,7 +207,7 @@ END%%

 %%ANKI
 Basic
-What does incrementing `NF` do?
+What two things does incrementing `NF` do?
 Back: Creates the field and rebuilds the record.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1707829863717-->
@ -215,7 +215,7 @@ END%%

 %%ANKI
 Basic
-What does decrementing `NF` do?
+What two things does decrementing `NF` do?
 Back: Throws away fields and rebuilds the record.
 Reference: Robbins, Arnold D. “GAWK: Effective AWK Programming,” October 2023. [https://www.gnu.org/software/gawk/manual/gawk.pdf](https://www.gnu.org/software/gawk/manual/gawk.pdf)
 <!--ID: 1707829863726-->
--- a/notes/logic/boolean-algebra.md
+++ b/notes/logic/boolean-algebra.md
@ -19,6 +19,14 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
 <!--ID: 1706994861304-->
 END%%

+%%ANKI
+Basic
+What set operation parallels conjunction?
+Back: $\cap$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1708221293474-->
+END%%
+
 %%ANKI
 Basic
 What name is given to $\lor$ operands?
@ -27,6 +35,14 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
 <!--ID: 1706994861306-->
 END%%

+%%ANKI
+Basic
+What set operation parallels disjunction?
+Back: $\cup$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1708221293479-->
+END%%
+
 %%ANKI
 Basic
 What C logical operator corresponds to $\neg$?
--- a/notes/logic/equiv-trans.md
+++ b/notes/logic/equiv-trans.md
@ -606,7 +606,7 @@ Basic
 What is the role of $E$ in textual substitution $E_e^x$?
 Back: It is the expression in which free occurrences of $x$ are replaced.
 Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1707762304126-->
+<!--ID: 1708347042194-->
 END%%

 %%ANKI
@ -614,7 +614,7 @@ Basic
 What is the role of $e$ role in textual substitution $E_e^x$?
 Back: It is the expression that is evaluated and substituted into $E$.
 Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1707762304127-->
+<!--ID: 1708347042199-->
 END%%

 %%ANKI
@ -622,7 +622,7 @@ Basic
 What is the role of $x$ in textual substitution $E_e^x$?
 Back: It is the identifier matching free occurrences in $E$ that are replaced.
 Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
-<!--ID: 1707762304129-->
+<!--ID: 1708347042203-->
 END%%

 %%ANKI
@ -651,7 +651,7 @@ END%%

 %%ANKI
 Basic
-Why might $E_e^x = E$ be an equivalence despite identifier $x$ existing in $E$?
+If $x \neq e$, why might $E_e^x = E$ be an equivalence despite $x$ existing in $E$?
 Back: If the only occurrences of $x$ in $E$ are bound.
 Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
 <!--ID: 1707762304135-->
@ -708,7 +708,7 @@ END%%
 %%ANKI
 Basic
 What is the role of $\bar{e}$ role in textual substitution $E_{\bar{e}}^{\bar{x}}$?
-Back: It is the expressions that are evaluated and substituted into $E$.
+Back: It is the expressions that are substituted into $E$.
 Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
 <!--ID: 1707762304127-->
 END%%
--- a/notes/posix/signals.md
+++ b/notes/posix/signals.md
@ -35,6 +35,21 @@ Tags: linux::cli
 <!--ID: 1706668253908-->
 END%%

+%%ANKI
+Basic
+What command can we run to print POSIX signals to the terminal?
+Back: `kill -l`
+Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
+<!--ID: 1708265979300-->
+END%%
+
+%%ANKI
+Cloze
+{`ascii`} is to ASCII as {`kill -l`} is to POSIX signals.
+Reference: Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
+<!--ID: 1708265979304-->
+END%%
+
 ### SIGHUP (1)

 A process receives a `SIGHUP` signal when the terminal it is attached to goes away before it finishes executing.
@ -143,4 +158,5 @@ END%%

 ## References

+* Cooper, Mendel. “Advanced Bash-Scripting Guide,” n.d., 916.
 * Dowling, “A List of Signals and What They Mean.”