Boolean Algebra is an algebra wherein values can be truth values ( or ) and operators are logical operators
A Proposition is a declarative statement that must be exactly one of TRUE or FALSE. The proposition’s truth value denotes the relation of a proposition to its

Logical Operators

Conjunction (AND) - denoted or for sequences It is true if and only if and are both .

P	Q
F	F	F
F	T	F
T	F	F
T	T	T

Disjunction (OR) - denoted or for sequences of propositions. It is true if at least one of and are true

P	Q
F	F	F
F	T	T
T	F	T
T	T	T

Negation (NOT) - denoted or sometimes . It is the opposite truth value to the value given

P
F	T
T	F

NAND - defined as the negation of the conjunction. It is false only when both inputs are true

P	Q
F	F	T
F	T	T
T	F	T
T	T	F

NOR - defined as the negation of the disjunction. It is true only when both inputs are false.

P	Q
F	F	T
F	T	F
T	F	F
T	T	F

Material Implication (IF) - denoted . It is defined by the following truth table

P	Q
F	F	T
F	T	T
T	F	F
T	T	T

Exclusive OR (XOR) - denoted or for sequences. It is defined as true if exactly an odd number of its inputs are true

P	Q
F	F	F
F	T	T
T	F	T
T	T	F

Bidirectional Implication (IFF / XNOR) - denoted or for sequences. It is defined as true if exactly an even number of its inputs are true

P	Q
F	F	T
F	T	F
T	F	F
T	T	T

Properties of Logical Operations

Logical operations satisfy the following properties

Double Negation

Identity

Domination

Complements

Commutativity

Associativity

Distributivity

Idempotence

Absorption

Redundancy

Consensus Law

De Morgan’s Laws

Monotonicity

Implications

Contraposition
Import-Export
Negation
Disjunction
Commutativity of antecedents
Distributivity

Links

Set Theory