If A = {x : x is a natural number}

B = {x : x is an even natural number}

C = {x : x is a prime number}, then find (A ∪ B) ∩ C
[4 Marks]

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Solution

A = {1, 2, 3, 4,........} ...(0.5 marks)

B = {2, 4, 6, 8,..........} ...(0.5 marks)

C = {2, 3, 5, 7, 11, 13,.........} ...(0.5 marks)

A ∪ B = {1, 2, 3, 4,........} ∪ {2, 4, 6, 8,..........}

= {1, 2, 3, 4,.....} ...(0.5 marks)

= A ...(0.5 marks)

(A ∪ B) ∩ C = A ∩ C ...(0.5 marks)

= {{1, 2, 3, 4,........} ∩ {2, 3, 5, 7,........}

= {2, 3, 5, 7, 11, 13,.........} ...(0.5 marks)

= C ...(0.5 marks)

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If A = {x: x is a natural number}

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If A = {x : x is a natural number}

B = {x : x is an even natural number}

C = {x : x is a prime number}, then (A ∪ B) ∩ C = ______________ .

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