Question

If $A,B$ and $C$ are three sets, then what is $A-(B-C)$ equal to?

• A. $A-(B\cap C)$
• B. $(A-B)\cup C$
• C. $(A-B)\cup (A\cap C)$
• D. $(A-B)\cup (A-C)$

Answer 1

The correct option is C

$(A-B)\cup (A\cap C)$

Explanation for the correct option:

We can see the Venn-diagram of $A-(B-C)$.

In the above Venn diagram, shaded area shows $A-(B-C)$

In the above Venn diagram, horizontal lines mean $(A-B)$ and vertical lines mean $(A\cap C)$

Total shaded portion $=\mathbf{(}\mathit{A}\mathbf{-}\mathit{B}\mathbf{)}\mathbf{\cup }\mathbf{(}\mathit{A}\mathbf{\cap }\mathit{C}\mathbf{)}$.

Hence, the option is$\left(C\right)$ correct.