If A = {1, 2, 3, 4, 5, 6}, how many subsets in P(A) have even cardinality?
Answer and explanation
Correct answer: 32
An n-element set has equally many subsets of even and odd cardinality. Since A has 6 elements, its total number of subsets is 2^6 = 64. Exactly half have even cardinality and half have odd cardinality, so the number of even-cardinality subsets is 64/2 = 32. This includes the empty set, whose cardinality is zero and is even.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
An n-element set has equally many subsets of even and odd cardinality. Since A has 6 elements, its total number of subsets is 2^6 = 64. Exactly half have even cardinality and half have odd cardinality, so the number of even-cardinality subsets is 64/2 = 32. This includes the empty set, whose cardinality is zero and is even.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
