Question

Let A, B, C be the subsets of the universal set X Let A' B' C' denote their complements in X Then which of below corresponds to the shaded portion in the given figure

• A. $A^{\prime }\cap B\cap C$
• B. $A\cap B^{\prime }\cap C$
• C. $A\cap B\cap C^{\prime }$
• D. $A^{\prime }\cap B^{\prime }\cap C$

Answer 1

The correct option is B $A\cap B^{\prime }\cap C$

The shaded region represents the intersection of A and c which is $A\cap C$.
Also, note that it does not include any part of B which is B'.
Hence, it is the intersection of the above two statements, which is $A\cap C\cap B^{\prime }$.