If A = {1, 2, 3}, what is the truth value of the statement {{1}, {2}} ⊆ P(A)?
Answer and explanation
Correct answer: True
The power set P(A) contains every subset of A. Since {1} ⊆ A and {2} ⊆ A, both {1} and {2} are elements of P(A). The set {{1}, {2}} has exactly these two elements, and each of them belongs to P(A). Therefore every element of {{1}, {2}} is an element of P(A), which proves that {{1}, {2}} ⊆ P(A). The statement is therefore true. It is important to distinguish {1} from 1: the power set contains sets such as {1}, not necessarily the number 1 as an element.
Frequently asked questions
What is the correct answer to this question?
True
Why is this the correct answer?
The power set P(A) contains every subset of A. Since {1} ⊆ A and {2} ⊆ A, both {1} and {2} are elements of P(A). The set {{1}, {2}} has exactly these two elements, and each of them belongs to P(A). Therefore every element of {{1}, {2}} is an element of P(A), which proves that {{1}, {2}} ⊆ P(A). The statement is therefore true. It is important to distinguish {1} from 1: the power set contains sets such as {1}, not necessarily the number 1 as an element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
