Q2 of 76 Page 2

If A = {2, 3}, B = {4, 5}, C = {5, 6} find A x (B ∪ C), (A x B) ∪ (A x C).

given: A = {2, 3}, B = {4, 5} and C = {5, 6}

To find: (A × B) ∪ (A × C)


Since, (B ∪ C) = {4, 5, 6}


∴A × (B ∪ C) = {(2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}


(A × B) = {(2, 4), (2, 5), (3, 4), (3, 5)}


(A × C) = {(2, 5), (2, 6), (3, 5), (3, 6)}


∴ (A × B) ∪ (A × C) = {(2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}


More from this chapter

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15

If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically:

i. A x B ii. B x A


iii A x A iv. B x B

 1

Given A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, find (A x B) ∩ (B x C).

 3

If A = {1, 2, 3}, B = {4}, c = {5}, then verify that:

i. A x ( B ∪ C) = (A x B) ∪ (A x C)


ii. A x (B ∩ C) = (A x B) ∩ (A x C)


iii. A x (B – C) = (A x B) – (A x C).

 4

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:

i. A x C B x D


ii. A x (B ∩ C) = (A x B) ∩ (A x C)