More natural deduction and term sheet overview.

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notes/_journal/2024-06/2024-06-23.md

@@ -9,5 +9,5 @@ title: "2024-06-23"
 - [ ] Korean (Read 1 Story)
 
 * Read chapter 4 ("Numbers") of "An Introduction to Ontology".
-* Notes on [[financing]] rounds.
+* Notes on [[financing-rounds]] rounds.
 * Additional notes on hash tables with [[closed-addressing#Chaining|chaining]] and independent uniform hashing.

notes/_journal/2024-07-22.md

@@ -9,3 +9,4 @@ title: "2024-07-22"
 - [ ] Korean (Read 1 Story)
 
 * Beginning notes on [[natural-deduction|natural deduction]].
+* Read chapter 3 "Overview of the Term Sheet" of "Venture Deals".

notes/formal-system/proof-system/natural-deduction.md

@@ -68,6 +68,11 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
 <!--ID: 1721655978506-->
 END%%
 
+### Negation
+
+For proposition $E1$, $$\neg{\text{-}}I{:} \quad \text{TODO}$$
+and $$\neg{\text{-}}E{:} \quad \text{TODO}$$
+
 ### Conjunction
 
 For propositions $E_1, \ldots, E_n$, $$\land{\text{-}}I{:} \quad \begin{array}{c} E_1, \ldots, E_n \\ \hline E_1 \land \cdots \land E_n \end{array}$$
@@ -174,6 +179,135 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
 <!--ID: 1721656601613-->
 END%%
 
+### Implication
+
+For propositions $E1$ and $E2$, $${\Rightarrow}{\text{-}}I: \quad \text{TODO}$$
+and $${\Rightarrow}{\text{-}}E: \quad \begin{array}{c} E1 \Rightarrow E2, E1 \\ \hline E2 \end{array}$$
+
+%%ANKI
+Basic
+In natural deduction, how is implication introduction denoted?
+Back: As ${\Rightarrow}{\text{-}}I$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665510225-->
+END%%
+
+%%ANKI
+Basic
+In natural deduction, how is implication elimination denoted?
+Back: As ${\Rightarrow}{\text{-}}E$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665541946-->
+END%%
+
+%%ANKI
+Basic
+*Modus ponens* is associated with which propositional logic operator?
+Back: $\Rightarrow$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665541949-->
+END%%
+
+%%ANKI
+Basic
+Does *modus ponens* correspond to an introduction or elimination rule?
+Back: Elimination.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665541951-->
+END%%
+
+%%ANKI
+Cloze
+Natural deduction rule {1:$\Rightarrow$}-{1:$E$} is also known as {modus ponens}.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665541953-->
+END%%
+
+%%ANKI
+Basic
+How is ${\Rightarrow}{\text{-}}E$ expressed in schematic notation?
+Back: $$\begin{array}{c} E1 \Rightarrow E2, E1 \\ \hline E2 \end{array}$$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665510228-->
+END%%
+
+%%ANKI
+Basic
+How is *modus ponens* expressed in schematic notation?
+Back: $$\begin{array}{c} E1 \Rightarrow E2, E1 \\ \hline E2 \end{array}$$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721665541955-->
+END%%
+
+%%ANKI
+Basic
+Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Rightarrow Q, P \\ \hline R \end{array}$$
+Back: N/A.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244354-->
+END%%
+
+%%ANKI
+Basic
+Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Rightarrow Q, P \\ \hline Q \end{array}$$
+Back: ${\Rightarrow}{\text{-}}E$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244357-->
+END%%
+
+### Biconditional
+
+For propositions $E1$ and $E2$, $${\Leftrightarrow}{\text{-}}I: \quad \begin{array}{c} E1 \Rightarrow E2, E2 \Rightarrow E1 \\ \hline E1 \Leftrightarrow E2 \end{array}$$
+and $${\Leftrightarrow}{\text{-}}E: \quad \begin{array}{c} E1 \Leftrightarrow E2 \\ \hline E1 \Rightarrow E2, E2 \Rightarrow E1 \end{array}$$
+
+%%ANKI
+Basic
+In natural deduction, how is biconditional introduction denoted?
+Back: As ${\Leftrightarrow}{\text{-}}I$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244359-->
+END%%
+
+%%ANKI
+Basic
+In natural deduction, how is biconditional elimination denoted?
+Back: As ${\Leftrightarrow}{\text{-}}E$.
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244361-->
+END%%
+
+%%ANKI
+Basic
+How is ${\Leftrightarrow}{\text{-}}I$ expressed in schematic notation?
+Back: $$\begin{array}{c} E1 \Rightarrow E2, E2 \Rightarrow E1 \\ \hline E1 \Leftrightarrow E2 \end{array}$$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244362-->
+END%%
+
+%%ANKI
+Basic
+Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Rightarrow Q, Q \Rightarrow P \\ \hline Q \Leftrightarrow P \end{array}$$
+Back: ${\Leftrightarrow}{\text{-}}I$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244367-->
+END%%
+
+%%ANKI
+Basic
+How is ${\Leftrightarrow}{\text{-}}E$ expressed in schematic notation?
+Back: $$\begin{array}{c} E1 \Leftrightarrow E2 \\ \hline E1 \Rightarrow E2, E2 \Rightarrow E1 \end{array}$$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244366-->
+END%%
+
+%%ANKI
+Basic
+Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Leftrightarrow Q \\ \hline Q \Rightarrow P \end{array}$$
+Back: ${\Leftrightarrow}{\text{-}}E$
+Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
+<!--ID: 1721666244364-->
+END%%
+
 ## Bibliography
 
 * Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

notes/startups/financing-rounds.md

@@ -1,5 +1,5 @@
 ---
-title: Financing
+title: Financing Rounds
 TARGET DECK: Obsidian::H&SS
 FILE TAGS: startups::financing
 tags:

notes/startups/term-sheet.md

@@ -0,0 +1,59 @@
+---
+title: Term Sheet
+TARGET DECK: Obsidian::H&SS
+FILE TAGS: startups::term-sheet
+tags:
+  - startups
+  - term-sheet
+---
+
+## Overview
+
+According to Feld et al., there are only two things VCs actually care about when making investments:
+
+* **Economics**: the return investors ultimately get in a liquidity event;
+* **Control**: mechanisms that allow investors to exercise control over the business and/or veto decisions the company can make. 
+
+%%ANKI
+Basic
+According to Feld et al. what two things do VCs *actually* care about when making investments?
+Back: Economics and control.
+Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
+<!--ID: 1721667425673-->
+END%%
+
+%%ANKI
+Basic
+VCs care about the economics of an investment. What does that refer to?
+Back: The return investors will receive in case of a liquidity event.
+Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
+<!--ID: 1721667425676-->
+END%%
+
+%%ANKI
+Basic
+What terms found in a term sheet relate to "economics"?
+Back: Those related to the return investors receive in a liquidity event.
+Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
+<!--ID: 1721667425682-->
+END%%
+
+%%ANKI
+Basic
+VCs care about the control of an investment. What does that refer to?
+Back: The ability to push and/or veto decisions made by the company.
+Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
+<!--ID: 1721667425684-->
+END%%
+
+%%ANKI
+Basic
+What terms found in a term sheet relate to "control"?
+Back: Those that effect investors ability to push and/or veto decisions.
+Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
+<!--ID: 1721667425679-->
+END%%
+
+## Bibliography
+
+* Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.