#### Negation (not) For a proposition $A$, $\neg A$ will represent the **negation**. |$A$|$\neg A$| |---|---| |T|F| |F|T| A proposition and its negation cannot be true at the same time Examples: 1. $A$ = The hat is on my head; $\neg A$ = The hat is not on my head. #### Conjunction "and" For 2 propositions A and B, $A \land B$ will represent the **conjunction**. |$A$|$B$|$A\land B$| |---|---|----------| |T|T|T| |T|F|F| |F|T|F| |F|F|F| Examples: 1. $A:x+1>x$ (True) $B: 2+1=3$ (True) $A\land B: 3>2$ (True) 2. $A:$ Tubas are musical instruments (True-ba) $B:$ All tubas are made of diamonds (False) $A \land B:$ Tubas are musical instruments made of diamonds (False) Tu-bad... #### Disjunction (Or) For 2 propositions A and B, $A \lor B$ will represent the **disjunction**. |$A$|$B$|$A\lor B$| |---|---|----------| |T|T|T| |T|F|T| |F|T|T| |F|F|F| #### Conditional (If-Then) For 2 Propositions A and B, $A\rightarrow B$ will represent the **conditional** |$A$|$B$|$A\rightarrow B$| |---|---|----------| |T|T|T| |T|F|F| |F|T|T| |F|F|T| #### Biconditional (If and only If) For 2 Propositions A and B, $A\leftrightarrow B$ will represent the **biconditional** |$A$|$B$|$A\rightarrow B$| |---|---|----------| |T|T|T| |T|F|F| |F|T|F| |F|F|T| If the biconditional of two statements is a [[Tautology]], then $A$ and $B$ are [[Logical Equivalence|equivalent]] It is equivalent to a [[#Conjunction and|conjunction]] of two [[#Conditional If-Then|conditionals]]