If A = {a, b, c}, why is {a, c} an element of P(A)?
Answer and explanation
Correct answer: Because it is a subset of A
A power set P(A) is the set of all subsets of A. The set {a,c} contains only elements that already belong to A = {a,b,c}; therefore {a,c} ⊆ A. It is consequently one of the members of P(A). It is not empty, it is not necessarily a complement, and no universal set U has been specified. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
Because it is a subset of A
Why is this the correct answer?
A power set P(A) is the set of all subsets of A. The set {a,c} contains only elements that already belong to A = {a,b,c}; therefore {a,c} ⊆ A. It is consequently one of the members of P(A). It is not empty, it is not necessarily a complement, and no universal set U has been specified. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
