If R and S are two reflexive relations on A, what can be said about R ∩ S?
Answer and explanation
Correct answer: R ∩ S is reflexive
Since R is reflexive on A, every self-pair (a, a) with a ∈ A belongs to R. Since S is also reflexive, the same self-pair belongs to S. Therefore every required self-pair belongs to both relations and consequently belongs to their intersection R ∩ S. This proves that R ∩ S is reflexive. The intersection need not be empty or equal to A, because relations consist of ordered pairs, not individual elements. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
R ∩ S is reflexive
Why is this the correct answer?
Since R is reflexive on A, every self-pair (a, a) with a ∈ A belongs to R. Since S is also reflexive, the same self-pair belongs to S. Therefore every required self-pair belongs to both relations and consequently belongs to their intersection R ∩ S. This proves that R ∩ S is reflexive. The intersection need not be empty or equal to A, because relations consist of ordered pairs, not individual elements. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
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