If and Only If

"A if and only if B" is a two-way conditional. It means "If A, then B" and "If B, then A" at the same time. The two claims always share the same truth value.

Example

"The light is green if and only if the system is armed." Either both are true or both are false.

See also

• Conditional Statement
• Contrapositive
• Necessary vs. Sufficient Conditions

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Last updated October 12, 2026