Which relation on A = {1,2,3} is symmetric?
Answer and explanation
Correct answer: {(1,2),(2,1),(3,3)}
To test symmetry, inspect every non-diagonal ordered pair and check whether its reverse is also present. In option A, (1,2) is accompanied by (2,1), and (3,3) is its own reverse, so the relation is symmetric. Option B lacks (2,1) and (3,2); C lacks (3,1) and (1,2); D lacks (3,2). Therefore only A satisfies the definition.
Frequently asked questions
What is the correct answer to this question?
{(1,2),(2,1),(3,3)}
Why is this the correct answer?
To test symmetry, inspect every non-diagonal ordered pair and check whether its reverse is also present. In option A, (1,2) is accompanied by (2,1), and (3,3) is its own reverse, so the relation is symmetric. Option B lacks (2,1) and (3,2); C lacks (3,1) and (1,2); D lacks (3,2). Therefore only A satisfies the definition.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
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