Identify disjoint pairs among given sets: Which of the following pairs are disjoint? (i) {1,2,3,4} and {x ∈ N : 4 ≤ x ≤ 6} (ii) {a, e, i, o, u} and {c, d, e, f} (iii) {x : x is even integer} and {x : x is odd integer}

Introduction / Context:
Disjoint sets have empty intersection. We check each pair for any shared elements.

Given Data / Assumptions:

• (i) {1,2,3,4} and {4,5,6}
• (ii) vowels and {c,d,e,f}
• (iii) even integers and odd integers

Concept / Approach:
Look for any common member between the two sets in each pair.

Step-by-Step Solution:
(i) Common element 4 → not disjoint(ii) Common element e → not disjoint(iii) No integer is both even and odd → disjoint

Verification / Alternative check:
Intersections: (i) {4}, (ii) {e}, (iii) ϕ.

Why Other Options Are Wrong:
They identify pairs that are not disjoint or select multiple when only one applies.

Common Pitfalls:
Overlooking boundary elements like 4 in (i).

Final Answer:
(iii)