# Get Answers to all your Questions

### Answers (1)

As we learnt in

REFLEXIVE RELATION -

A relation R in A is said to be reflexive,  if a R a ,∀ a ∈ A

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SYMMETRIC RELATION -

A relation R in A is said to be symmetric, if a R b ⇒ b R a,∀ a,b ∈ A

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TRANSITIVE RELATION -

A relation R in A is said to be transitive, if a R b and b R c ⇒ a R c ∀ a,b,c ∈ A

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S = {y = x + 1        0 < x < 2}

T = {x - y is an integer}

For T :     (a, a) it is integer reflexive

(a, b) (b, a) it is integer symmetric.

(a, b) (b, c) (a, c) it is integer transitive.

So it is equivalence

For S : x = 1,  y = 2 not equivalence.

Correct option is 1.

Option 1)

is an equivalence relation on but is not

This is the correct option.

Option 2)

Neither nor   is an equivalence relation on

This is an incorrect option.

Option 3)

Both and are equivalence relations on

This is an incorrect option.

Option 4)

is an equivalence relation on but is not

This is an incorrect option.

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