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

If A = {0, ∅, {0}}, how many elements does A have?

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Answer and explanation

Correct answer: 3

The outer braces define the set A. Inside them are three distinct objects: the number 0, the empty set ∅, and the singleton set {0}. Although {0} contains 0 as its own element, it is not the same object as 0. Likewise, ∅ is a set with no elements. Thus A has three elements, so its cardinality is 3.

Tags

setscardinalityempty-setset-elementsThe 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?

3

Why is this the correct answer?

The outer braces define the set A. Inside them are three distinct objects: the number 0, the empty set ∅, and the singleton set {0}. Although {0} contains 0 as its own element, it is not the same object as 0. Likewise, ∅ is a set with no elements. Thus A has three elements, so its cardinality is 3.

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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