Question
Download Solution PDFIf A is a non-empty set such that the power set of A is P(A) = {ϕ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}} then find the set A ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Power Set:
Let A be set, then the set of all the possible subsets of A is called the power set of A and is denoted by P(A).
Note: If A is a finite set with m elements. Then the number of elements (cardinality) of the power set of A is given by: n (P(A)) = 2m.
CALCULATION:
Given: A is a non-empty set such that the power set of A is P(A) = {ϕ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}
Here, we have to find the set A
As we know that, if A is a set then the power set of A is given by P(A) = {X : X ⊆ A}
So, we can clearly see from the definition of the power set of A that A = {1, 2, 3}
Hence, the correct option is 3.
Last updated on Jun 30, 2025
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