(Anb)'=A'ub'

Question

This question is from chap "sets" and the answer is kinda long so plz answere

Answer 1

In the diagram, sets A and B are shown as two circles interlocking. The logical space is divided into distinct regions such that U=W+X+Y+Z where U is the universal set. A=X+Y and B=Y+Z.

Y=A∩B and Y'=W+X+Z.

A'=W+Z and B'=W+X.

Y'=W+X+Z.

A'∪B'=(W+Z)∪(W+X)=W+X+Z=Y', so (A∩B)'=A'∪B' QED