Q1 of 76 Page 2

If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).

Here, A={1,2,4} ,B={2,4,5} ,C={2,5}

So, A ∖ C={1,2,4} ∖ {2,5}

={1,4}

Also,B ∖ C={2,4,5}∖ {2,5}

={4}

Now, (A ∖ B)×(B ∖ C)={(x,y):xϵ(A∖ C) and yϵ(B∖ C) }

={(1,4), (4,4)}

For the relation R₁ defined on R by the rule (a, b) R₁ 1 + ab > 0. Prove that: (a, b) R₁ and (b,c) R₁ (a, c) R₁ is not true for all a, b, c R.

Let R be a relation on N x N defined by (a, b) R (c, d) a + d = b + c for all (a, b), (c, d) N x N.

Show that:

i. (a, b) R (a, b) for all (a, b) N x N

ii. (a, b) R (c, d) (c, d) R (a, b) for all (a, b), (c, d) N x N

iii. (a, b) R (c, d) and (c, d) R (e, f) (a, b) R (e, f) for all (a, b), (c, d), (e, f) N × N

If n(A) = 3, n(B) = 4, ten write n (A × A × B).