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Question

Which of the following pair of sets is disjoint?

A

A = {3, 4, 5, 6, 7} and B = {x : x is a natural number and 7 x 10}

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B

P = {x : x is a prime number} and Q = {x : x is an even number}

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C

S = {x : x is an odd number} and T = {x : x is an even number}

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D
None of the above
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Solution

The correct option is C S = {x : x is an odd number} and T = {x : x is an even number} a) A = {3, 4, 5, 6, 7} B = {x : x is a natural number and 7 ≤ x ≤ 10} = {7, 8, 9, 10} A ∩ B = {3, 4, 5, 6, 7} ∩ {7, 8, 9, 10} = {7}. So, A and B are not disjoint sets. b) P = {2, 3, 5, 7, 11,......} ; Q = {2, 4, 6, 8, 10,........} P ∩ Q = {2, 3, 5, 7, 11,......} ∩ {2, 4, 6, 8, 10,........} = {2} So, given sets P and Q are not disjoint sets. c) S = {1, 3, 5, 7, - - - -} ; T = {2, 4, 6, 8, 10,........} S ∩ T = {1, 3, 5, 7, - - - -} ∩ {2, 4, 6, 8, 10,........} = { } ∴ S and T are disjoint sets.

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