If S = {a, b, c}, Then the power set of S  is P(S) =  { ∅, a, b, c, {a,b}, {a,c}, {b,c}, {a, b, c} }Group startsTrue or FalseTrue, unselectedFalse, unselected

Identification of the Problem

We need to determine whether the given power set description of S = {a, b, c} is accurate.

Relevant Concepts

The power set of a set S includes all possible subsets of S, including the empty set and the set itself. For a set with n elements, the power set will have $2^n$ subsets.

Analysis

1. Set S: The original set is S = {a, b, c}.
2. Number of Elements: The set S has 3 elements.
3. Calculating the Power Set: The number of subsets can be calculated as: $2^3 = 8$
4. Enumerating the Power Set:
   • The subsets include:
     • The empty set: $\emptyset$
     • Single elements: {a}, {b}, {c}
     • Two-element subsets: {a, b}, {a, c}, {b, c}
     • The set itself: {a, b, c}

Listing all subsets: The power set P(S) can be represented as: $P(S) = \{ \emptyset, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\} \}$

Verification and Summary

The provided power set in the question is: $P(S) = \{ \emptyset, a, b, c, \{a,b\}, \{a,c\}, \{b,c\}, \{a, b, c\} \}$ This contains the elements a, b, and c not nested in curly braces, which is incorrect.

Final Answer

False