Which of the following pairs of sets are disjoint
Question:

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) {aeiou}and {cdef}

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

Solution:

(i) {1, 2, 3, 4}

{xx is a natural number and 4  x  6} = {4, 5, 6}

Now, {1, 2, 3, 4}  {4, 5, 6} = {4}

Therefore, this pair of sets is not disjoint.

(ii) {aeiou (cdef} = {e}

Therefore, {aeiou} and (cdef} are not disjoint.

(iii) {xx is an even integer}  {xx is an odd integer} = Φ

Therefore, this pair of sets is disjoint.