Q8 of 65 Page 56

If A × B = {(–2, 3), (–2, 4), (0, 4), (3, 3), (3, 4), find A and B.

Here, A × B = {(–2, 3), (–2, 4), (0, 4), (3, 3), (3, 4)}

To find: A and B

Clearly, A is the set of all first entries in ordered pairs in A × B

∴ A = {-2, 0, 3}

and B is the set of all second entries in ordered pairs in A × B

∴ B = {3, 4}

If A = {1, 3, 5) B = {3, 4} and C = {2, 3}, verify that:

(i) A × (B ∪ C) = (A × B) ∪ (A × C)

(ii) A × (B ∩ C) = (A × B) ∩ (A × C)

Let A = {x ϵ W : x < 2}, B = {x ϵ N : 1 < x ≤ 4} and C = {3, 5}. Verify that:

(i) A × (B ∪ C) = (A × B) ∪ (A × C)

(ii) A × (B ∩ C) = (A × B) ∩ (A × C)

Let A = {2, 3} and B = {4, 5}. Find (A × B). How many subsets will (A × B) have?

Let A × B = {(a, b): b = 3a – 2}. if (x, –5) and (2, y) belong to A × B, find the values of x and y.