# Equivalent Propositions

## Equivalent Propositions

Propositions that have the same truth value.

Synonym for identity.

### Symbol

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”.

### Examples

• 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”.