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Question
If R and S are relations on a set A, then prove that R is reflexive and S is any relation ⇒ R ∪ S is reflexive ?
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Solution
R is reflexive and S is any relation.
Suppose a ∈ A. Then,
(a, a) ∈ R [Since R is reflexive]
⇒ (a, a) ∈ R ∪ S
⇒ R ∪ S is reflexive on A.
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