Question

Determine whether the given set is the power set of some set. If the set is a power set, give the set of which it is a power set.

Set: {∅,{a},{b},{a,b}}
A) Yes, {a,b}
B) Yes, {a}
C) No
D) Yes, {∅}{∅}

Answer 1

The given set {∅,{a},{b},{a,b}} is not the power set of any set.

Step-by-step explanation:

The given set, {∅,{a},{b},{a,b}}, is not the power set of any set. To be a power set, it must contain all possible subsets of a given set. In this case, the set contains the empty set, {∅}, the set {a}, the set {b}, and the set {a,b}, but it is missing the set {a,b} – the two-element set that would complete the power set. Therefore, the answer is No.