How many elements are in the set A = {x : x ∈ ℕ and x² < 10}?
Answer and explanation
Correct answer: 3
Taking ℕ = {1, 2, 3, ...}, test the natural numbers in order. We have 1² = 1 < 10, 2² = 4 < 10, and 3² = 9 < 10, while 4² = 16 is not less than 10. Thus A = {1, 2, 3}, so it contains exactly three elements. If a convention includes 0 in ℕ, 0² also satisfies the condition; however, the options and standard school convention here use ℕ beginning with 1.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Taking ℕ = {1, 2, 3, ...}, test the natural numbers in order. We have 1² = 1 < 10, 2² = 4 < 10, and 3² = 9 < 10, while 4² = 16 is not less than 10. Thus A = {1, 2, 3}, so it contains exactly three elements. If a convention includes 0 in ℕ, 0² also satisfies the condition; however, the options and standard school convention here use ℕ beginning with 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
