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Implicative Laws

Proposition: For all formulas A and B, we have

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

Implication can thus be defined by negation and disjunction.

Proposition: Implication is not associative.

Proof: by construction of a counterexample:

• Meaning of F => (F => F) is true.
• Meaning of (F => F) => F is false.