Logic

# Logical Operations and Truth Tables

## Keywords: logic, true, false, negation, disjunction, conjunction, implication, equality

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 (∨) (or)

 P Q P∨Q $\top$ $\top$ $\top$ $\top$ $\perp$ $\top$ $\perp$ $\top$ $\top$ $\perp$ $\perp$ $\perp$

Conjunction (∧) (and)

 P Q P∧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 (⇔) (biconditional)

 P Q P⇔Q $\top$ $\top$ $\top$ $\top$ $\perp$ $\perp$ $\perp$ $\top$ $\perp$ $\perp$ $\perp$ $\top$