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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 4

Let A = {x ∈ ℕ : 1 ≤ x ≤ 50 and x is divisible by 7}, where ℕ = {1, 2, 3, …}. What is n(A)?

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Answer and explanation

Correct answer: 7

The positive multiples of 7 that do not exceed 50 are 7, 14, 21, 28, 35, 42, and 49. The next multiple, 56, is greater than 50, so it is excluded. Thus A has seven elements, and its cardinality is n(A) = 7. The explicit positive-number convention also prevents 0 from being counted.

Tags

setsfinite setcardinalitymultiples of 7The Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

7

Why is this the correct answer?

The positive multiples of 7 that do not exceed 50 are 7, 14, 21, 28, 35, 42, and 49. The next multiple, 56, is greater than 50, so it is excluded. Thus A has seven elements, and its cardinality is n(A) = 7. The explicit positive-number convention also prevents 0 from being counted.

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.

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