Q. 11

# Show that the rel

Given: (a, b) S (c, d) a + d = b + c

To prove: given relation is equivalence relation

A relation is said to be an equivalence relation if it is reflexive, symmetric and transitive

Step 1:

Now, (a, b) S (b, a)

a + b = b + a which is true

Relation R is reflexive

Step 2:

Now, (a, b) S (c, d)

a + b = c + d

c + d = a + b

(c, d) S (a, b) which is true

Relation R is symmetric

Step 3:

Now, (a, b) S (c, d) and (c, d) S (e, f)

a + b = c + d and c + d = e + f

a + b = e + f

(a, b) S (e, f) which is true

Relation R is transitive

This shows that Relation S is an equivalence relation

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