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Equivalence Laws

Proposition: For all formulas A and B, the following holds:

A <=> B	iff	B <=> A
A <=> B	iff	(A /\  B) \/ (~A /\  ~B)
A <=> B	iff	(A => B) /\  (B => A)

Equivalence can thus be defined by implication and conjunction.

Proposition: Equivalence is not associative.

Proof: by construction of a counterexample.