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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 6

If A = {x ∈ N : x is divisible by 5 and x ≤ 100}, what is n(A)?

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Answer and explanation

Correct answer: 20

The natural-number elements of A are the positive multiples of 5 not exceeding 100: 5, 10, 15, ..., 100. Each multiple has the form 5k, where k = 1, 2, ..., 20. Equivalently, the number of terms is 100 ÷ 5 = 20. Because 100 itself is divisible by 5 and satisfies x ≤ 100, it is included.

Tags

setsfinite setscardinalitymultiplesThe 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?

20

Why is this the correct answer?

The natural-number elements of A are the positive multiples of 5 not exceeding 100: 5, 10, 15, ..., 100. Each multiple has the form 5k, where k = 1, 2, ..., 20. Equivalently, the number of terms is 100 ÷ 5 = 20. Because 100 itself is divisible by 5 and satisfies x ≤ 100, it is included.

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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