Logical conjunction
In logic and mathematics, and is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true. The logical connective that represents this operator is typically written as ∧ or ⋅ .
"A and B" is true only if A is true and B is true.
An operand of a conjunction is a conjunct.
Related concepts in other fields are:
And is usually denoted by an infix operator: in mathematics and logic, ∧ or × ; in electronics, ⋅ ; and in programming languages, &, &&, or and. In Jan Łukasiewicz's prefix notation for logic, the operator is K, for Polish koniunkcja.
Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.
The conjunctive identity is 1, which is to say that AND-ing an expression with 1 will never change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result 1.
The truth table of :
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