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Question

# If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number } and D = {x : x is a prime number}, find : (i) A∩B (ii) A∩C (iii) A∩D (iv) B∩C (v) B∩D (vi) C∩D

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Solution

## Here A = {x : x is a natural number} = {1, 2, 3, 4, 5, ............} B = {x : x is an even natural number} = {2, 4, 6, .............} C = {x : x is a an odd natural number} = {1, 3, 5, 7, ............} and D = {x : x is a prime number} = {2, 3, 5, 7, ............} (i) A∩B = {x : x is a natural number} ∩ {x : x is an even natural number} = {x : x is an even natural number} = B (ii) A∩C = {x : x is a natural number} ∩ {x : x is an odd natural number} = {x : x is an odd natural number} = C (iii) A∩D = {x : x is a natural number} ∩ {x : x is a prime number} = {x : x is a prime number} = D (iv) B∩C = {x : x is an even natural number} ∩ {x : x is an odd natural number} = Φ (v) B∩D = {x : x is an even natural number} ∩ {x : x is a prime number} = {2} (vi) C∩D = {x : x is an odd natural number} ∩ {x : x is a prime number} = {x : x is an odd prime number} = D -{2}

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