If A = {a,b,c,d}, how many elements of P(A) do not contain a and have odd size?
Answer and explanation
Correct answer: 4
Any required subset must exclude a, so only the three-element set {b,c,d} is available. We need its subsets of odd size. Among a three-element set, the odd-sized subsets consist of the three one-element subsets and the one three-element subset, for a total of 3 + 1 = 4. Equivalently, half of the 2³ = 8 subsets have odd cardinality, giving 2² = 4. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Any required subset must exclude a, so only the three-element set {b,c,d} is available. We need its subsets of odd size. Among a three-element set, the odd-sized subsets consist of the three one-element subsets and the one three-element subset, for a total of 3 + 1 = 4. Equivalently, half of the 2³ = 8 subsets have odd cardinality, giving 2² = 4. Hence 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.
