If A = {g, h, i, j}, how many elements of P(A) are also proper subsets of A?
Answer and explanation
Correct answer: 15
A has 4 elements, so its power set P(A) contains 2^4 = 16 subsets in total. A proper subset is a subset that is not equal to the original set A. Among the 16 power-set elements, only A itself is not proper. Removing it leaves 16 − 1 = 15 proper subsets. Therefore, option B is correct; the empty set is also a proper subset.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A has 4 elements, so its power set P(A) contains 2^4 = 16 subsets in total. A proper subset is a subset that is not equal to the original set A. Among the 16 power-set elements, only A itself is not proper. Removing it leaves 16 − 1 = 15 proper subsets. Therefore, option B is correct; the empty set is also a proper subset.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
