Power set of C = {1, {2}}: Write P(C) explicitly.

Introduction / Context:
The power set of a set with two elements has 2^2 = 4 subsets. When one element is itself a set, we still treat it as an atomic element during subset formation. We must list all combinations of including or excluding each of the two elements 1 and {2}.

Given Data / Assumptions:

• C = {1, {2}}
• Subsets are formed by choosing each element or not

Concept / Approach:
Enumerate subsets: choose neither element (ϕ); choose only 1 ({1}); choose only {2} ({{2}}); choose both ({1, {2}}). Collect these into P(C).

Step-by-Step Solution:
ϕ{1}{{2}}{1, {2}}

Verification / Alternative check:
Count check: 4 subsets as required for 2 elements.

Why Other Options Are Wrong:
(a) and (c) omit required subsets; (d) is not needed because (b) is correct and complete.

Common Pitfalls:
Confusing element {2} with the number 2, or forgetting the subset containing both elements.

Final Answer:
{ϕ, {1}, {{2}}, {1, {2}}}