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Let X be the set of all citizens of India. Elements x, y in X

Question

Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct ?

A

The relation is an equivalence relation on X.

B

The relation is symmetric but neither reflexive nor transitive.

C

The relation is reflexive but neither symmetric nor transitive.

D

None of the above

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Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct ?

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Text solutionVerified

given that,

X = {All citizens of India}

and R=

{(x, y) : x, yϵ X, ∣ x - y ∣ = 5}

i) For reflexive

∣ x - x ∣ = 0 \neq = 5

∴ (x, x) \in R

So,

R

is not reflexive

ii) For symmetric

Let

x R y \Rightarrow ∣ x - y ∣ = 5 \Rightarrow ∣ y - x ∣ = 5

\Rightarrow y R x

So,

R

is symmetric

iii) For transitive

Let

x, y, z \in X

such that

x R y \Rightarrow ∣ x - y ∣ = 5

and

y R z \Rightarrow ∣ y - z ∣ = 5

But

∣ x - z ∣ \neq = 5

So,

R

is not transitive

Hence, the relation is symmetric but neither reflexive nor transitive

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Question Text	Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct ?
Answer Type	Text solution:1
Upvotes	150