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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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