If A has 4 elements, how many non-empty proper subsets does A have?
Advertisement
Answer and explanation
Correct answer: 14
A set with n elements has 2^n total subsets because each element can either be included or excluded. For n = 4, the total number is 2^4 = 16. A non-empty proper subset excludes both the empty set and the complete set A. Hence the required number is 16 − 2 = 14, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
A set with n elements has 2^n total subsets because each element can either be included or excluded. For n = 4, the total number is 2^4 = 16. A non-empty proper subset excludes both the empty set and the complete set A. Hence the required number is 16 − 2 = 14, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement