If a set has 4 elements, how many elements will its power set contain?
Answer and explanation
Correct answer: 16
If a finite set has n elements, its power set contains all possible subsets, and the number of these subsets is 2ⁿ. For n = 4, the number is 2⁴ = 2 × 2 × 2 × 2 = 16. This count includes the empty set and the original set itself, as well as all subsets containing one, two, or three elements. Therefore, option C, 16, is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
If a finite set has n elements, its power set contains all possible subsets, and the number of these subsets is 2ⁿ. For n = 4, the number is 2⁴ = 2 × 2 × 2 × 2 = 16. This count includes the empty set and the original set itself, as well as all subsets containing one, two, or three elements. Therefore, option C, 16, is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
