Question

The set represented by the shaded portion of the below Venn - diagram is ___.

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

Answer 1

The correct option is C

$B^{\prime }\cap (A\cup C{)}^{\prime }$

The below given Venn diagram represents the set $B^{\prime },$ the set of elements outside of B.

The Venn diagram below stands for $B^{\prime }\cup (A\cup C{)}^{\prime },$ the set of elements belonging to B' or $(A\cup C{)}^{\prime }.$

$B^{\prime }\cap (A\cup C{)}^{\prime }$ is the set of elements belonging to B' and $(A\cup C{)}^{\prime },$ shown below.

$A\cup B\cup C$ is the set of elements belonging to A or B or C, illustrated below.