Question

The value of $(A\cup B\cup C)$ intersection ( $A$ intersection $B^C$ intersection $C^C$)${}^C$ intersection $C^C$ is,

• A. $B\cap C^C$
• B. $B^C\cap C^C$
• C. $B\cap C$
• D. $A\cap B\cap C$

Answer 1

The correct option is A

$B\cap C^C$

Explanation for correct answer

We are given three different sets and we need to find their intersection.

Given different sets are $(A\cup B\cup C)$, ${\left(A\cap B^C\cap C^C\right)}^C$ and $C^C$

Here, the entire Venn diagram represents $(A\cup B\cup C)$

The colors excluding yellow color represents ${\left(A\cap B^C\cap C^C\right)}^C$

and, $C^C$ is represented by yellow $+$ pink $+$ red

Now, we need to find the intersection of these three sets, that is, $(A\cup B\cup C)\cap {\left(A\cap B^C\cap C^C\right)}^C\cap C^C$

This can be represented by pink $+$ red, that is, $B\cap C^C$

Hence, the correct option is (A) i.e. $B\cap C^C$.