Question

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

• A. $A$ is always a subset of the complement of $B$
• B. $B$ is always a subset of $A$
• C. $A$ and $B$ are always disjoint
• D. $A$ and the complement of $B$ are always non disjoint

Answer 1

Answer: (D)

Since, $A$ is not a subset of $B$.
$\therefore$ Some elements of $A$ will not be elements of $B$. Hence, $A$ and complement of $B$ are always non-disjoint.