If T₁ = {x : x ∈ ℕ, x ≤ 40, and x leaves remainder 2 when divided by 5}, how many elements are in T₁?
Answer and explanation
Correct answer: 8
The natural numbers that leave remainder 2 upon division by 5 have the form 5k + 2. Up to 40, they are 2, 7, 12, 17, 22, 27, 32, and 37. The next number, 42, exceeds the bound 40 and must be excluded. Thus T₁ contains eight distinct elements, so option B is correct. The upper bound makes this otherwise repeating pattern finite.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The natural numbers that leave remainder 2 upon division by 5 have the form 5k + 2. Up to 40, they are 2, 7, 12, 17, 22, 27, 32, and 37. The next number, 42, exceeds the bound 40 and must be excluded. Thus T₁ contains eight distinct elements, so option B is correct. The upper bound makes this otherwise repeating pattern finite.
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.
