If n(A) = 6, how many elements of P(A) are subsets with an even number of elements?
Answer and explanation
Correct answer: 32
A six-element set has 2⁶ = 64 subsets in total. The subsets can be paired with their complements. Because the set has six elements, the complement of an even-sized subset is also even-sized, while the standard binomial identity shows that even- and odd-sized subsets occur equally often. Therefore half of 64, namely 2⁵ = 32, have even cardinality. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
A six-element set has 2⁶ = 64 subsets in total. The subsets can be paired with their complements. Because the set has six elements, the complement of an even-sized subset is also even-sized, while the standard binomial identity shows that even- and odd-sized subsets occur equally often. Therefore half of 64, namely 2⁵ = 32, have even cardinality. 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.
