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==Logical negation==
==Logical negation==
''[[Logical negation]]'' is an [[logical operation|operation]] on one [[logical value]], typically the value of a [[proposition]], that produces a value of ''true'' when its operand is false and a value of ''false'' when its operand is true.
The truth table of '''NOT p''' (also written as '''~p''' or '''¬p''') is as follows:
The truth table of '''NOT p''' (also written as '''~p''' or '''¬p''') is as follows:
==Logical conjunction==
==Logical conjunction==
''[[Logical conjunction]]'' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are true.
The truth table of '''p AND q''' (also written as '''p ∧ q''', '''p & q''', or '''p<math>\cdot</math>q''') is as follows:
The truth table of '''p AND q''' (also written as '''p ∧ q''', '''p & q''', or '''p<math>\cdot</math>q''') is as follows:
==Logical disjunction==
==Logical disjunction==
''[[Logical disjunction]]'', also called ''logical alternation'', is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are false.
The truth table of '''p OR q''' (also written as '''p ∨ q''') is as follows:
The truth table of '''p OR q''' (also written as '''p ∨ q''') is as follows:
==Logical equality==
==Logical equality==
''[[Logical equality]]'' is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both operands are false or both operands are true.
The truth table of '''p EQ q''' (also written as '''p = q''', '''p ↔ q''', or '''p ≡ q''') is as follows:
The truth table of '''p EQ q''' (also written as '''p = q''', '''p ↔ q''', or '''p ≡ q''') is as follows:
==Exclusive disjunction==
==Exclusive disjunction==
''[[Exclusive disjunction]]'', also known as ''logical inequality'' or ''symmetric difference'', is an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' just in case exactly one of its operands is true.
The truth table of '''p XOR q''' (also written as '''p + q''', '''p ⊕ q''', or '''p ≠ q''') is as follows:
The truth table of '''p XOR q''' (also written as '''p + q''', '''p ⊕ q''', or '''p ≠ q''') is as follows:
==Logical implication==
==Logical implication==
The '''[[logical implication]]''' and the '''[[material conditional]]''' are both associated with an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if the first operand is true and the second operand is false.
The ''[[logical implication]]'' and the ''[[material conditional]]'' are both associated with an [[logical operation|operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if the first operand is true and the second operand is false.
The truth table associated with the material conditional '''if p then q''' (symbolized as '''p → q''') and the logical implication '''p implies q''' (symbolized as '''p ⇒ q''') is as follows:
The truth table associated with the material conditional '''if p then q''' (symbolized as '''p → q''') and the logical implication '''p implies q''' (symbolized as '''p ⇒ q''') is as follows:
==Logical NAND==
==Logical NAND==
The '''[[logical NAND]]''' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are true. In other words, it produces a value of ''true'' if and only if at least one of its operands is false.
The ''[[logical NAND]]'' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''false'' if and only if both of its operands are true. In other words, it produces a value of ''true'' if and only if at least one of its operands is false.
The truth table of '''p NAND q''' (also written as '''p | q''' or '''p ↑ q''') is as follows:
The truth table of '''p NAND q''' (also written as '''p | q''' or '''p ↑ q''') is as follows:
==Logical NNOR==
==Logical NNOR==
The '''[[logical NNOR]]''' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are false. In other words, it produces a value of ''false'' if and only if at least one of its operands is true.
The ''[[logical NNOR]]'' is a [[logical operation]] on two [[logical value]]s, typically the values of two [[proposition]]s, that produces a value of ''true'' if and only if both of its operands are false. In other words, it produces a value of ''false'' if and only if at least one of its operands is true.
The truth table of '''p NNOR q''' (also written as '''p ⊥ q''' or '''p ↓ q''') is as follows:
The truth table of '''p NNOR q''' (also written as '''p ⊥ q''' or '''p ↓ q''') is as follows:
