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diff --git a/content/Class Notes/MATH 109 Lecture 2.md b/content/Class Notes/MATH 109 Lecture 2.md
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+---
+tags:
+- "Type/Note"
+- "Topic/Mathematics"
+- "Class/MATH_109"
+date:
+- 2024-09-30
+---
+
+## Priority of logical connectors
+
+high to low: $\neg$, $\land$, $\lor$
+
+$(\neg P) \lor Q$
+
+Implication: $\implies$
+
+In $P \implies Q$:
+- $P$ is called the **hypothesis**
+- $Q$ is called the **conclusion**
+
+Ways to read $P\implies Q$
+- $P$ implies $Q$
+- If $P$ then $Q$
+- $Q$ if $P$
+- $P$ only if $Q$
+- $Q$ whenever $P$
+- $P$ is sufficient for $Q$
+- $Q$ is necessary for $P$
+
+The **converse** of $P\implies Q$ is $Q\implies P$  
+The **negation** of $P\implies Q$ is $\neg (P\implies Q)$  
+The **contrapositive** of $P\implies Q$ is $\neg Q\implies \neg P$
+
+Equivalence: $\iff$
+$P\iff Q$ reads as:
+- $P$ is equivalent to $Q$
+- $P$ is necessary and sufficient for $Q$
+- $P$ if and only if $Q$
+- $P$ iff $Q$
+- $P$ precisely when $Q$
+
+| $P$ | $Q$ | $P \iff Q$ |
+| --- | --- | --- |
+| T | T | T |
+| T | F | F |
+| F | T | F |
+| F | F | T |
+
+$P \iff Q$ is true when $P$, $Q$ have the same truth value.
+
+$P\iff Q$ is the same as $(P\implies Q)\land (Q\implies P)$
+
+When $P\iff Q$ is true, we say $P$, $Q$ are **logically equivalent**
+
+> [!definition] Logically Equivalent
+> Two statements $P$, $Q$ are logically equivalent if $P\iff Q$ is always true for all possibilities of atomic statement truth value combinations
+
+Example: $P\iff Q$ is logically equivalent to $Q\iff P$
+
+To verify, we check $(P \iff Q) \iff ((P \implies Q) \land (Q \implies P))$ is true
+
+| $P$ | $Q$ | $P\iff Q$ | $Q\iff P$ | $(P \iff Q) \iff ((P \implies Q) \land (Q \implies P))$ |
+| --- | --- | --- | --- | --- |
+| T | T | T | T | T |
+| T | F | F | F | T |
+| F | T | F | F | T |
+| F | F | T | T | T |
diff --git a/content/Daily Notes/2024-09-30.md b/content/Daily Notes/2024-09-30.md
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+---
+tags:
+- "Daily_Note"
+---
+
+- [[MATH 109 Lecture 2]]