Q.

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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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 is D.

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Detailed Solution

∴A is not a subset of B   ∴ Some point of A will not be a point of B, So that point will being to complement of B  . Hence A and complement of B are always non-disjoint
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Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then