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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 ? - Mathematics

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प्रश्न

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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उत्तर

R is reflexive and S is any relation.

Suppose a A. Then,

 (a, a∈ R                        [Since R is reflexive]

⇒ (a, a∈ ∪ S

⇒ R S is reflexive on A.

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पाठ 1: Relations - Exercise 1.2 [पृष्ठ २७]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 1 Relations
Exercise 1.2 | Q 15.2 | पृष्ठ २७

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