Which statement about ∅ and {∅} is correct?
Answer and explanation
Correct answer: {∅} has one element
The governing distinction is between an empty set and a set containing the empty set. The symbol ∅ has no elements, so its cardinality is 0. In {∅}, the empty set itself appears as one element, so the cardinality is 1. The braces do not mean that the inside is empty; they form a new set whose member is ∅. Therefore ∅ and {∅} are different, and option C is correct.
Frequently asked questions
What is the correct answer to this question?
{∅} has one element
Why is this the correct answer?
The governing distinction is between an empty set and a set containing the empty set. The symbol ∅ has no elements, so its cardinality is 0. In {∅}, the empty set itself appears as one element, so the cardinality is 1. The braces do not mean that the inside is empty; they form a new set whose member is ∅. Therefore ∅ and {∅} are different, and option C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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