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If A = {x ∈ W : 5 < x < 10}, B = {3, 4, 5, 6, 7} and C = {x = 2n; n ∈ N and n ≤4}. Find:

**(A ∩ B) ∪ (A ∩ C)**

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#### Solution

A = {x ∈ W : 5 < x < 10}

= {6, 7, 8, 9}

B = {3, 4, 5, 6, 7}

C = {x = 2n; n ∈ N and n ≤4}

x = 2n

When n = 1,

x = 2 x 1

= 2

When n = 2,

x = 2 x 2

= 4

When n = 3,

x = 2 x 3

= 6

When n =4,

x = 2 x 4

= 8

∴ C = {2, 4, 6, 8}

(A ∩ B)

= {6, 7, 8, 9} ∩ {3, 4, 5, 6, 7}

= {6, 7}

∴ (A ∩ B) ∪ (A ∩ C)

= {6, 7} ∪ {6, 8}

= {6, 7, 8}

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