For which value of n(A) will the power set P(A) have exactly 16 elements?
Answer and explanation
Correct answer: n(A) = 4
If a finite set A has n elements, then its power set P(A) has 2ⁿ elements because each element independently has two choices: it may be included in a subset or excluded. We need 2ⁿ = 16. Since 16 = 2⁴, n = 4. Thus P(A) has exactly 16 members when A contains four elements. The other choices give 4, 8, and 256 subsets respectively.
Frequently asked questions
What is the correct answer to this question?
n(A) = 4
Why is this the correct answer?
If a finite set A has n elements, then its power set P(A) has 2ⁿ elements because each element independently has two choices: it may be included in a subset or excluded. We need 2ⁿ = 16. Since 16 = 2⁴, n = 4. Thus P(A) has exactly 16 members when A contains four elements. The other choices give 4, 8, and 256 subsets respectively.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
