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Proof

Proof: We prove associativity. Take arbitrary formulas A, B, and C. We show that A /\  (B /\  C) and (A /\  B) /\  C have same truth value.

A	B	C	B /\  C	A /\  (B /\  C)	A /\  B	(A /\  B) /\  C
false	false	false	false	false	false	false
false	false	true	false	false	false	false
false	true	false	false	false	false	false
false	true	true	true	false	false	false
true	false	false	false	false	false	false
true	false	true	false	false	false	false
true	true	false	false	false	true	false
true	true	true	true	true	true	true