Spot the Faulty Step

Difficulty: Medium · Topics: Discrete Mathematics, Sets, Set Operations

A and B are subsets of the universal set E. Which of the computations below, carried out with the distributive law, are wrong ?

I. Acup(A'cap B')=(Acup A')cap(Acup B')=Ecap(Acup B')=Acup B'

II. (Acap B)cup(Acap B')=Acap(Bcup B')=Acap E=E

III. (Mcup N')cap(Ncup M)=(Ncap N')cup M=varnothingcup M=M