If A = {0, 1, 2, 3}, how many elements of P(A), that is, subsets of A, have sum 3?
Answer and explanation
Correct answer: 4
The elements of P(A) are all subsets of A. We need to list subsets whose elements add to 3: {3}, {0, 3}, {1, 2}, and {0, 1, 2}. These are four different subsets. The zero element is important because adding 0 does not change a subset’s sum, so it creates an additional valid subset from both {3} and {1, 2}. No other subset has sum 3. Therefore, the correct answer is option C, 4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The elements of P(A) are all subsets of A. We need to list subsets whose elements add to 3: {3}, {0, 3}, {1, 2}, and {0, 1, 2}. These are four different subsets. The zero element is important because adding 0 does not change a subset’s sum, so it creates an additional valid subset from both {3} and {1, 2}. No other subset has sum 3. Therefore, the correct answer is option C, 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
