Q. 145.0( 1 Vote )

# Mark the tick aga

According to the question ,

R = {(a, b) , (c, d) : a + d = b + c }

Formula

For a relation R in set A

Reflexive

The relation is reflexive if (a , a) R for every a A

Symmetric

The relation is Symmetric if (a , b) R , then (b , a) R

Transitive

Relation is Transitive if (a , b) R & (b , c) R , then (a , c) R

Equivalence

If the relation is reflexive , symmetric and transitive , it is an equivalence relation.

Check for reflexive

Consider , (a, b) R (a, b)

(a, b) R (a, b) a + b = a + b

which is always true .

Therefore , R is reflexive ……. (1)

Check for symmetric

(a, b) R (c, d) a + d = b + c

(c, d) R (a, b) c + b = d + a

Both the equation are the same and therefore will always be true.

Therefore , R is symmetric ……. (2)

Check for transitive

(a, b) R (c, d) a + d = b + c

(c, d) R (e, f) c + f = d + e

On adding these both equations we get , a + f = b + e

Also,

(a, b) R (e, f) a + f = b + e

It will always be true

Therefore , R is transitive ……. (3)

Now , according to the equations (1) , (2) , (3)

Correct option will be (D)

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