If A = {1, 2, 3, 4}, how many subsets of P(A) contain 1 but do not contain 4?
Advertisement
Answer and explanation
Correct answer: 4
For a subset of A, the inclusion of 1 is compulsory and the exclusion of 4 is compulsory. Thus only 2 and 3 remain undecided. Each of these two elements has two independent choices: it may be included or omitted. Therefore the number of permitted subsets is 2 × 2 = 2² = 4. They are {1}, {1,2}, {1,3}, and {1,2,3}.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a subset of A, the inclusion of 1 is compulsory and the exclusion of 4 is compulsory. Thus only 2 and 3 remain undecided. Each of these two elements has two independent choices: it may be included or omitted. Therefore the number of permitted subsets is 2 × 2 = 2² = 4. They are {1}, {1,2}, {1,3}, and {1,2,3}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement