Comparable sets (subset or superset relation exists): Which pair of sets is comparable (i.e., one is a subset of the other)?

Introduction / Context:
Two sets are comparable if one is contained in the other. This checks basic understanding of subset relations and differences between elements and sets-as-elements.

Given Data / Assumptions:

• (a) A = {1, 3, 5}, B = {2, 3, 5, 6}
• (b) A = {x ∈ N : x ≤ 10} = {1,2,…,10}, B = {1,2,…,10,11}
• (c) A includes the element {4,5}, not two separate elements 4 and 5

Concept / Approach:
Check whether every element of one set is in the other (subset test) for each pair.

Step-by-Step Solution:
(a) Neither contains the other (1 ∉ B and 2,6 ∉ A)(b) {1..10} ⊂ {1..11} → comparable(c) {4,5} as a single element prevents A ⊆ B or B ⊆ A

Verification / Alternative check:
Count and membership checks confirm only (b) satisfies comparability.

Why Other Options Are Wrong:
(a) lacks mutual containment; (c) confuses element vs subset; 'Both (a) and (b)' is invalid because (a) fails.

Common Pitfalls:
Misreading {4,5} as two elements instead of one element which is itself a set.

Final Answer:
A = {x: x ∈ N and x ≤ 10}, B = {1, 2, 3, …, 10, 11}