If A = {a, b, c, d}, how many subsets contain at least one of a or b?
Answer and explanation
Correct answer: 12
A set with four elements has 2^4 = 16 total subsets. To count subsets containing at least one of a or b, use the complement: subsets containing neither a nor b can use only c and d, so there are 2^2 = 4 such subsets. Therefore, the required number is 16 − 4 = 12. This method avoids double-counting subsets that contain both a and b.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
A set with four elements has 2^4 = 16 total subsets. To count subsets containing at least one of a or b, use the complement: subsets containing neither a nor b can use only c and d, so there are 2^2 = 4 such subsets. Therefore, the required number is 16 − 4 = 12. This method avoids double-counting subsets that contain both a and b.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
