Question

Identify the shaded region in the figure, where $A$ and $B$ are two sets represented by the circles and $U$ is the universal set, which is represented by the rectangle.

• A. $B-A$
• B. $B-(A\cup B)$
• C. $A-(A\cup B)$
• D. $U-B^{\prime }-(A\cap B)$

Answer 1

Answer: (A), (D)

$U-B^{\prime }-(A\cap B)$

The region in the figure consists of the elements of B alone.
$B-A$ is the set of all elements of $B,$ but not of $A.$

This is exactly what we have in the figure where $A\cap B$ is removed from $B.$

The last option also gives the same set. When we subtract $B^{\prime }$ from the universal set $U,$ we get $B.$

So the expression $U-B^{\prime }-(A\cap B)$ becomes $B-(A\cap B).$ This is same as $B-A.$