Let X be the set of all persons living in a city. Persons x, y X are said to be related as x < y if y is at least 5 years older than x . Which one of - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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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 x < y if y is at least 5 years older than x . Which one of the following is correct?

Solution & Step-by-step Explanation

The relation R is defined as: x R y ⟺ y \geq x + 5 .Reflexive: For a relation to be reflexive, x R x must hold, which means x \geq x + 5 . This is 0 \geq 5, which is false. Thus, it is not reflexive.Symmetric: For a relation to be symmetric, x R y ⟹ y R x . If y \geq x + 5, then x \leq y - 5 . This means x cannot be \geq y + 5 . Thus, it is not symmetric.Transitive: If x R y and y R z, then z \geq y + 5 and y \geq x + 5 .Substituting y : z \geq (x + 5) + 5 ⟹ z \geq x + 10 Since z \geq x + 10 certainly implies z \geq x + 5, the relation x R z holds. Thus, it is transitive.

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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 x < y if y is at least 5 years older than x . Which one of the following is correct?

The relation is an equivalence relation on X .

The relation is transitive but neither reflexive nor symmetric.

The relation is reflexive but neither transitive nor symmetric.

The relation is symmetric but neither transitive nor reflexive.

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