Equivalent Propositions

Equivalent Propositions

Propositions that have the same truth value.

Synonym for identity.


The equivalence of the two propositions P and Q is noted as: P \(\iff\) Q and is read as: “P is equivalent to Q” or “P if and only if Q”.


  • For the real values of x, the following propositions are equivalent:
    4x + 2 = 12   \(\iff\)   x = 2.5.
  • “The triangles ABC and DEF are similar” \(\iff\) “The corresponding angles of triangles ABC and DEF are isometric”.

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