Let N = {1, 2, 3, ...} be the set of positive natural numbers and A = {x : x ∈ N and x² < 10}. Which of the following is a proper subset of A?
Answer and explanation
Correct answer: {1, 3}
Since x is a positive natural number and x² < 10, the possible values are x = 1, 2, and 3, because 1² = 1, 2² = 4, and 3² = 9, while 4² = 16 is not less than 10. Thus A = {1,2,3}. A proper subset must be contained in A but must not be equal to A. Only {1,3} satisfies both conditions. Option A equals A, option B contains 4, and option D contains 0, so the correct answer is C.
Frequently asked questions
What is the correct answer to this question?
{1, 3}
Why is this the correct answer?
Since x is a positive natural number and x² < 10, the possible values are x = 1, 2, and 3, because 1² = 1, 2² = 4, and 3² = 9, while 4² = 16 is not less than 10. Thus A = {1,2,3}. A proper subset must be contained in A but must not be equal to A. Only {1,3} satisfies both conditions. Option A equals A, option B contains 4, and option D contains 0, so the correct answer is C.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
