Power set of a set that contains a set element: Find P(A) for A = {{a, b}, c}, i.e., list all subsets of A.

Introduction / Context:The power set P(A) is the set of all subsets of A. When A contains a set element like {a,b}, remember that subsets must be formed from the elements {{a,b}, c} rather than from a and b individually.

Given Data / Assumptions:

• A = {{a, b}, c}

Concept / Approach:Elements of A are exactly two objects: E1 = {a,b} and E2 = c. Thus P(A) must contain 2^2 = 4 subsets built from E1 and E2.

Step-by-Step Solution:P(A) = { ϕ, {{a, b}}, {c}, {{a, b}, c} }Compare with options: none lists exactly these four subsets using correct braces.

Verification / Alternative check:Count check: power set must have 4 members; any option with a different count or with {a,b} (not wrapped as an element) is incorrect.

Why Other Options Are Wrong:They misuse {a,b} as if a and b were elements of A directly; valid subsets must consist of elements {{a,b}, c}.

Common Pitfalls:Confusing elements inside the inner set {a,b} with elements of A itself.

Final Answer:None of these