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 $B$ $(A 
ot\subseteq B)$.This implies that there exists at least one element $x$ such that $x \in A$ and $x 
o

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given that $A$ is not a subset of $B$ $(A 
ot\subseteq B)$.This implies that 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 $B$ in $X$).Thus,$x \in A \cap B^c$.Since there exists at least one element in the intersection of $A$ and $B^c$,the sets $A$ and $B^c$ are 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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