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Symbolic Logic

Conjunction (AND statements)

Aconjunctionis a compound statement formed by combining two statements using the wordand．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)

Adisjunctionis a compound statement formed by combining two statements using the wordand．在数理逻辑中,迪sjunction 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)

Thenegationof a statement$p$is不$p$．

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

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