If A = {a, b, c}, how many subsets in P(A) contain at least one of a or b?
Answer and explanation
Correct answer: 6
The set A has three elements, so its power set contains 2^3 = 8 subsets. To count subsets containing at least one of a or b, subtract the subsets that contain neither a nor b. If neither a nor b is selected, only c may be selected or omitted, giving two subsets: the empty set and {c}. Thus, the required number is 8 - 2 = 6. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The set A has three elements, so its power set contains 2^3 = 8 subsets. To count subsets containing at least one of a or b, subtract the subsets that contain neither a nor b. If neither a nor b is selected, only c may be selected or omitted, giving two subsets: the empty set and {c}. Thus, the required number is 8 - 2 = 6. Therefore, option 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.
