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
$⊤$	$⊥$
$⊥$	$⊤$

Disjunction (∨) (or)

P	Q	P∨Q
$⊤$	$⊤$	$⊤$
$⊤$	$⊥$	$⊤$
$⊥$	$⊤$	$⊤$
$⊥$	$⊥$	$⊥$

Conjunction (∧) (and)

P	Q	P∧Q
$⊤$	$⊤$	$⊤$
$⊤$	$⊥$	$⊥$
$⊥$	$⊤$	$⊥$
$⊥$	$⊥$	$⊥$

Implication (⇒) (if ..., than...)

P	Q	P⇒Q
$⊤$	$⊤$	$⊤$
$⊤$	$⊥$	$⊥$
$⊥$	$⊤$	$⊤$
$⊥$	$⊥$	$⊤$

Equality (⇔) (biconditional)

P	Q	P⇔Q
$⊤$	$⊤$	$⊤$
$⊤$	$⊥$	$⊥$
$⊥$	$⊤$	$⊥$
$⊥$	$⊥$	$⊤$

General Information
Symbols, relationships
Number theory
Number Sets
Prime Numbers - Prime Factorization
Divisibility Rules
Greatest Common Divisor (factor) - Least Common Multiple
Operations with rational numbers
Binomial theorem
Binomial theorem
Combinatorics
Permutations
Combination
Variation
Sets
Operations on Sets
Fundamental laws of set algebra
Cardinality of sets
Cartesian product
Relation
Logic
Logical Operations and Truth Tables
Properties of Logical Operators
Graph Theory
Graph Theory - definitions, relationships