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implication

Symbol $\implies$ — a one-way "if the left side is true, the right side must be true."

$P \implies Q$ asserts that whenever statement $P$ is true, statement $Q$ is also true. It says nothing about the reverse direction ( $Q \implies P$ , the converse, is a separate claim).

Examples

$a < b \text{ and } c < 0 \implies ac > bc$ .