Answer :

**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**

Rate this question :

Fill in theMathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

Let A = {1, 2, 3}Mathematics - Exemplar

Show that the relMathematics - Board Papers

Let N denote the Mathematics - Board Papers