Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
(i) A × (B ∩ C) = (A × B) ∩ (A × C)
(ii) A × C is a subset of B × D

Solution:

(i) To verify: A x (B ∩ C) = (A x B) ∩ ( A x C)

We have B ∩ C = {1, 2, 3, 4} ∩ {5, 6} = Φ

LHS = A x (B ∩ C)

= A x Φ

= Φ

Now,

A x B = {(1, 1), (1, 2), (1, 3), (1, 4), (2,1), (2, 2), (2, 3), (2, 4)}

A x C = {(1, 5), (1, 6), (2, 5), (2, 6)}

Therefore,

RHS = (A x B) ∩ (A x C)

= Φ

Therefore, L.H.S. = R.H.S

Hence, A x (B ∩ C) = (A ∩ B) ∩ (A ∩ C)

(ii) To verify: A x C is a subset of B x D.

We have

A x C = {(1, 5), (1, 6), (2, 5), (2, 6)}

B x D = {(1, 5),(1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)}

We can observe that all the elements of set A x C are the elements of set B x D .

Therefore, A x C is a subset of B x D

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NCERT Solutions Class 11 Maths Chapter 2 Exercise 2.1 Question 7

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D

Summary:

A = {1, 2}, B = {1, 2, 3, 4} , C = {5, 6} and D = {5, 6, 7, 8} is given. We have found that A × C is a subset of B × D