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Symbolic Logic

Conjunction (AND statements)

A conjunction is a compound statement formed by combining two statements using the word and . In symbolic logic, the conjunction of $p$ and $q$ is written $p\wedge q$ .

A conjunction is true only if both the statements in it are true. The following truth table gives the truth value of $p\wedge q$ depending on the truth values of $p$ and $q$ .

$\begin{array}{ccc}p& q& p\wedge q\\ \text{T}& \text{T}& \text{T}\\ \text{T}& \text{F}& \text{F}\\ \text{F}& \text{T}& \text{F}\\ \text{F}& \text{F}& \text{F}\end{array}$

Disjunction (OR statements)

A disjunction is a compound statement formed by combining two statements using the word and . In symbolic logic, the disjunction of $p$ and $q$ is written $p\vee q$ .

A disjunction is true if either one or both of the statements in it is true. The following truth table gives the truth value of $p\vee q$ depending on the truth values of $p$ and $q$ .

$\begin{array}{ccc}p& q& p\vee q\\ \text{T}& \text{T}& \text{T}\\ \text{T}& \text{F}& \text{T}\\ \text{F}& \text{T}& \text{T}\\ \text{F}& \text{F}& \text{F}\end{array}$

Negation (NOT statements)

The negation of a statement $p$ is not $p$ .

The symbol $\sim$ or $\neg$ is used to denote negation.

If $p$ is true, then $\sim p$ is false, and vice versa.