# Logical Operations and Truth Tables

A mathematical sentence is a sentence that states a fact or contains a complete idea. A sentence that can be judged to be true or false is called a statement.
The statement can be true (T) or false (⊥).
P, Q, R,... statements

Example:
This girl is beatiful. - not a statement.
Today is Wensday. - statement.

## Negation ($¬$) (not)

 $P$ $¬P$ $\top$ $\perp$ $\perp$ $\top$

## Disjunction ($\vee$) (or)

 $P$ $Q$ $P\vee Q$ $\top$ $\top$ $\top$ $\top$ $\perp$ $\top$ $\perp$ $\top$ $\top$ $\perp$ $\perp$ $\perp$

## Conjunction ($\wedge$) (and)

 $P$ $Q$ $P\wedge Q$ $\top$ $\top$ $\top$ $\top$ $\perp$ $\perp$ $\perp$ $\top$ $\perp$ $\perp$ $\perp$ $\perp$

## Implication ($⇒$) (if ... than...)

 $P$ $Q$ $P⇒Q$ $\top$ $\top$ $\top$ $\top$ $\perp$ $\perp$ $\perp$ $\top$ $\top$ $\perp$ $\perp$ $\top$

## Equality ($⇔$) (if and only if)

 $P$ $Q$ $P⇔Q$ $\top$ $\top$ $\top$ $\top$ $\perp$ $\perp$ $\perp$ $\top$ $\perp$ $\perp$ $\perp$ $\top$
Keywords: logic, true, false, negation, disjunction, conjunction, implication, equality