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Conditional Statement

p \rightarrow q

If p and q are statement variables, the conditional of q by p is “If p then q” or “p implies q.” If p is true and q is false the statement is false; otherwise it is true. “p” is the hypothesis (or antecedent) of the conditional and “q” the conclusion (or consequent).

\displaystyle p

\displaystyle q

\displaystyle p \rightarrow q

T T T
T F F
F T T
F F T