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Logical conditional Redirected from Material implication
In logical calculus of mathematics, logical conditional is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion[?] (or consequent). The operator is denoted using an left-arrow "->".
The hypothesis is sometimes also called "necessary condition" while the conclusion may be called "sufficient condition".
It is defined using the following truth table:
p q | p -> q
----+--------
T T | T
T F | F
F T | T
F F | T
In the case that the hypothesis is true, the result is the same as conclusion. Otherwise, the whole statement is true regardless the value of conclusion.
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