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) \(C ∩ D\)

Answer 1

A = {x: x is a natural number} = {1, 2, 3, 4, 5 ...}
B = {x: x is an even natural number} = {2, 4, 6, 8 ...}
C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 ...}
D = {x: x is a prime number} = {2, 3, 5, 7 ...}

(i) \(A ∩B\) = {x: x is a even natural number} = B

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(ii) \(A ∩C\) = {x: x is an odd natural number} = C

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(iii) \(A ∩D\) = {x: x is a prime number} = D

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(iv) \(B ∩C = \phi\)

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(v) \(B ∩D\) = {2}

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(vi) \(C ∩D\) = {x: x is odd prime number}