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) {a, e, i, o, u} and {c, d, e, f}
(iii) {x : x is an even integer} and {x : x is an odd integer}

Answer 1

Answer: Two sets are disjoint if they have no elements in common.

(i) The first set is {1, 2, 3, 4} and the second set is {x : x is a natural number and 4 ≤ x ≤ 6}. The second set contains the numbers 4, 5, and 6. The first set contains the number 4. Therefore, the two sets have one element in common, which means they are not disjoint.

(ii) The first set is {a, e, i, o, u} and the second set is {c, d, e, f}. The two sets have the letter "e" in common, but no other elements in common. Therefore, they are not disjoint.

(iii) The first set is {x : x is an even integer} and the second set is {x : x is an odd integer}. Even and odd integers have different parity, so they have no elements in common. Therefore, these two sets are disjoint.

In summary, the only pair of sets that are disjoint is the set of even integers and the set of odd integers.

Explanation: