I must prove the most basic associativity in boolean algebra and there is two equation to be proved:
(1) a+(b+c) = (a+b)+c (where + indicates OR). (2) a.(b.c) = (a.b).c (where . indicates AND).
I have a hint to solve this: You can prove that both sides in (1) are equal to [a+(b+c)].[(a+b)+c] (I'm pretty sure that it's coming from idempotency.).
We can use all axioms of boolean algebra: distributivity, commutativity, complements, identity elements, null elements, absorption, idempotency, a = (a')' theorem, a+a'b = a + b theorem (' indicates NOT) except De Morgan's Law. Also duality of boolean algebra for sure.
Please help. Thanks in advance.