If A has 6 elements, how many subsets of A do not contain a particular chosen element?
Answer and explanation
Correct answer: 32
Exclude the specified element from every allowed subset. The remaining set has 6 − 1 = 5 elements, and each of these five elements may be included or excluded independently. Therefore the number of permitted subsets is 2^5 = 32. Equivalently, the 2^6 = 64 subsets of A split equally into those containing the chosen element and those not containing it. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Exclude the specified element from every allowed subset. The remaining set has 6 − 1 = 5 elements, and each of these five elements may be included or excluded independently. Therefore the number of permitted subsets is 2^5 = 32. Equivalently, the 2^6 = 64 subsets of A split equally into those containing the chosen element and those not containing it. Thus 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.
