Question

Which of the following pairs of sets are disjoint. a) {1,2,3,4} and {x:x is a natural number and 4 <=x<=6}.b){a,e,i,o,u} and {c, d, e, f}.c){x:x is an even integer} and {x:x is an odd integer}.
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Answer 1

Which of the following pairs of sets are disjoint

(i) {1,2,3,4} and {x:x is a natural number and 4≤x≤6}

(ii) { a,e,i,o,u } and { c,d,e,f }

(iii) {x:x is an even integer } and {x:x is an odd integer}

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Solution

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(i) A={1,2,3,4}

B={x:x is a natural number and 4≤x≤6}={4,5,6}

Now, A∩B={1,2,3,4}∩{4,5,6}={4}

Therefore, this pair of sets are not disjoint.

(ii) A={a,e,i,o,u}

B={c,d,e,f}

A∩B={e}

Therefore, this pair of sets are not disjoint.

(iii) A={x:x is an even integer}

B={x:xis an odd integer}

A∩B=ϕ

Therefore, this pair of sets is disjoint.