Let A={1,2,3,4,5} and define aRb if and only if a+b is odd. Which statement correctly describes this relation?
Answer and explanation
Correct answer: It is symmetric and irreflexive but not transitive.
The correct answer is C. If a+b is odd, then b+a is also odd, so the relation is symmetric. For every a, a+a=2a is even, never odd; therefore no element is related to itself and the relation is irreflexive. It is not transitive: 1R2 and 2R3 are true, but 1R3 is false because 1+3=4 is even. Hence it cannot be an equivalence relation, and options A, B, and D are incorrect.
Frequently asked questions
What is the correct answer to this question?
It is symmetric and irreflexive but not transitive.
Why is this the correct answer?
The correct answer is C. If a+b is odd, then b+a is also odd, so the relation is symmetric. For every a, a+a=2a is even, never odd; therefore no element is related to itself and the relation is irreflexive. It is not transitive: 1R2 and 2R3 are true, but 1R3 is false because 1+3=4 is even. Hence it cannot be an equivalence relation, and options A, B, and D are incorrect.
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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