If |A| = 8, how many subsets in P(A) have even cardinality?
Answer and explanation
Correct answer: 128
A set with 8 elements has 2^8 = 256 total subsets. For every nonempty finite set, the subsets with even cardinality and the subsets with odd cardinality occur in equal numbers. Thus the number of even-cardinality subsets is 2^8/2 = 2^7 = 128. The empty set is included because its cardinality is zero, which is even. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
128
Why is this the correct answer?
A set with 8 elements has 2^8 = 256 total subsets. For every nonempty finite set, the subsets with even cardinality and the subsets with odd cardinality occur in equal numbers. Thus the number of even-cardinality subsets is 2^8/2 = 2^7 = 128. The empty set is included because its cardinality is zero, which is even. 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.
