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

If A = {∅, {∅}}, what is n(A), the number of elements in A?

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Answer and explanation

Correct answer: 2

The outer set A has two elements: the empty set ∅ and the singleton set {∅}. These are different objects. The symbol ∅ denotes a set with no elements, whereas {∅} denotes a set whose one element is the empty set. Since the two outer elements are distinct, n(A) = 2.

Tags

setsempty setcardinalitysingleton setThe 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?

2

Why is this the correct answer?

The outer set A has two elements: the empty set ∅ and the singleton set {∅}. These are different objects. The symbol ∅ denotes a set with no elements, whereas {∅} denotes a set whose one element is the empty set. Since the two outer elements are distinct, n(A) = 2.

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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