If A = {1, 3, 9}, how many subsets in P(A) contain {1, 9}?
Answer and explanation
Correct answer: 2
A subset of A that contains {1, 9} must include both 1 and 9. The remaining element, 3, is optional: it may be excluded, giving {1, 9}, or included, giving {1, 3, 9}. Thus there are 2 valid subsets. Equivalently, one free element gives 2^1 = 2 choices. The question asks for subsets containing the set {1, 9}, not subsets containing only those two elements.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
A subset of A that contains {1, 9} must include both 1 and 9. The remaining element, 3, is optional: it may be excluded, giving {1, 9}, or included, giving {1, 3, 9}. Thus there are 2 valid subsets. Equivalently, one free element gives 2^1 = 2 choices. The question asks for subsets containing the set {1, 9}, not subsets containing only those two elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
