Power set construction for a 2-element set: Write the power set of A = {8, 9} (i.e., the set of all subsets of A, including the empty set and A itself).

Introduction / Context:The power set of a set A is the set of all its subsets. For a set with n elements, the power set has 2^n subsets, including the empty set and A itself.

Given Data / Assumptions:

• A = {8, 9}
• n = 2 elements

Concept / Approach:List all subsets of a 2-element set: the empty subset, both singleton subsets, and the full set.

Step-by-Step Solution:Subsets: ϕ, {8}, {9}, {8, 9}Power set P(A) = {ϕ, {8}, {9}, {8, 9}}

Verification / Alternative check:Count check: 2^2 = 4 subsets appear, as required.

Why Other Options Are Wrong:{ϕ, {8}, {9}} omits {8, 9}; {{8, 9}, {8}} is incomplete; 'All of these' cannot be correct because the listed options are not all valid power sets.

Common Pitfalls:Forgetting to include the empty set, or thinking order matters (it does not in sets).

Final Answer:{ϕ, {8}, {9}, {8, 9}}