If a set has 4 elements, how many subsets does it have?
Answer and explanation
Correct answer: 16
For a set with n elements, each element has two independent choices when forming a subset: it may be included or excluded. Thus the total number of subsets is 2ⁿ. With n = 4, the number is 2⁴ = 2 × 2 × 2 × 2 = 16. This count includes both the empty set, in which no element is selected, and the original set, in which all four elements are selected. Therefore C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
For a set with n elements, each element has two independent choices when forming a subset: it may be included or excluded. Thus the total number of subsets is 2ⁿ. With n = 4, the number is 2⁴ = 2 × 2 × 2 × 2 = 16. This count includes both the empty set, in which no element is selected, and the original set, in which all four elements are selected. Therefore C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
