Let A and B be two non-empty subsets of a set | vedclass

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(D) Given that $A$ is not a subset of $B$ $(A 
ot\subseteq B)$.By definition, this means there exists at least one element $x$ such that $x \in A$ an

Vedclass · Accepted Answer

$A$ and the complement of $B$ are always non-disjoint

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(D) Given that $A$ is not a subset of $B$ $(A 
ot\subseteq B)$.By definition, this means there exists at least one element $x$ such that $x \in A$ and $x 
otin B$.Since $x 
otin B$, it follows that $x \in B^c$ (where $B^c$ is the complement of $B$ with respect to $X$).Therefore, there exists an element $x$ such that $x \in A$ and $x \in B^c$.This implies that the intersection $A \cap B^c$ is non-empty $(A \cap B^c 
eq \emptyset)$.Thus, $A$ and the complement of $B$ are always non-disjoint.

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

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