If A = {1,3,5,7}, what are the total number of subsets and the number of one-element subsets in P(A), respectively?
Answer and explanation
Correct answer: 16 and 4
The set A has four elements. For a finite set with n elements, the power set contains 2^n subsets, because each element can either be included or excluded. Thus P(A) has 2^4 = 16 subsets. A one-element subset is formed by choosing exactly one of the four elements, so there are 4 such subsets: {1}, {3}, {5}, and {7}. Therefore the answer is 16 and 4.
Frequently asked questions
What is the correct answer to this question?
16 and 4
Why is this the correct answer?
The set A has four elements. For a finite set with n elements, the power set contains 2^n subsets, because each element can either be included or excluded. Thus P(A) has 2^4 = 16 subsets. A one-element subset is formed by choosing exactly one of the four elements, so there are 4 such subsets: {1}, {3}, {5}, and {7}. Therefore the answer is 16 and 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
