Q5 of 50 Page 14

Let U = {4, 8, 12, 16, 20, 24, 28}, A = {8, 16, 24} and B = {4, 16, 20, 28}. Find (A ∪ B)’ and (A ∩ B)’

(i) Consider A ⋃ B,


⇒ A ⋃ B = {8, 16, 24} ⋃ {4, 16, 20, 28} = {4, 8, 16, 20, 24, 28}


Now, (A ⋃ B)’ = U {4, 8, 16, 20, 24, 28} = {12}


(ii) Consider A ⋂ B,


⇒ A ⋂ B = {8, 16, 24} ⋂ {4, 16, 20, 28} = {16}


Now, (A ⋃ B)’ = U {16} = {4, 8, 12, 20, 24, 28}


More from this chapter

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3

Draw Venn diagram of three sets A,B and C illustrating the following:

(i) A ∩ B ∩ C


(ii) A and B are disjoint but both are subsets of C


(iii) A ∩ (BC)


(iv) (B ∪ C)A


(v) A∪(B ∪ C)


(vi) C ∪ (BA)


(vii) C ∩ (B ∪ A)

 4

Use Venn diagram to verify (A ∩ B) ∪ (AB) = A.

 6

Given that U = {a, b, c, d, e, f, g, h}, A = {a, b, f, g}, and B = {a, b, c}, verify De Morgan’s laws of complementation.

 7

Verify De Morgan’s laws for set difference using the sets given below:

A = {1, 3, 5, 7, 9, 11, 13, 15}, B = {1, 2, 5, 7} and C = {3, 9, 10, 12, 13}.