On A={1,2}, which property is satisfied by R={(1,1),(1,2),(2,1)}?
Answer and explanation
Correct answer: R is symmetric
R is symmetric because whenever (1,2) belongs to R, its reverse pair (2,1) also belongs to R; the pair (1,1) is automatically its own reverse. It is not reflexive because (2,2) is absent, and it is not antisymmetric because both (1,2) and (2,1) occur with distinct elements. Hence it cannot be an equivalence relation.
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What is the correct answer to this question?
R is symmetric
Why is this the correct answer?
R is symmetric because whenever (1,2) belongs to R, its reverse pair (2,1) also belongs to R; the pair (1,1) is automatically its own reverse. It is not reflexive because (2,2) is absent, and it is not antisymmetric because both (1,2) and (2,1) occur with distinct elements. Hence it cannot be an equivalence relation.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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