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Let X be the set of all persons living in a city. Persons x, y in X are said to be related as `xlty` if y is at least 5 years older than x. Which one of the following is correct?A. The relation is an equivalence relation on X.B. The relation is transitive but neither reflexive nor symmetricC. The relation is reflexive but neither transitive nor symmetricD. The relation is symmetric but neither transitive nor reflexive |
Answer» Correct Answer - B Given that `xlty if y ge x +5` For Reflexive: `x cancellt x` Hence, relation is not reflexive. For Symmetry: if `xlty`, then `y cancellt x` Hence, relation is not symmetry. For Transitive: if `x lt y and y lt z`, then `x lt z` Hence, relation is transitive. |
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