If A = {1,2,3,4,5,6}, how many subsets in P(A) contain 1 and have even cardinality?
Answer and explanation
Correct answer: 16
Because 1 must be included, one element is already fixed in every permitted subset. For the total cardinality to be even, the chosen number of elements from the remaining five elements {2,3,4,5,6} must be odd. Among five elements, the number of subsets with odd cardinality equals the number with even cardinality, namely 2⁵ ÷ 2 = 16. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Because 1 must be included, one element is already fixed in every permitted subset. For the total cardinality to be even, the chosen number of elements from the remaining five elements {2,3,4,5,6} must be odd. Among five elements, the number of subsets with odd cardinality equals the number with even cardinality, namely 2⁵ ÷ 2 = 16. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
