Which statement is false for the empty set?
Answer and explanation
Correct answer: It is equal to {0}
The empty set, written as ∅, contains no elements, so its cardinality is 0. It is also finite because a finite set has a limited number of elements, including zero elements. However, {0} is not empty: it contains the number 0 as one element and therefore has cardinality 1. Thus the statement that the empty set equals {0} is false. The symbols ∅ and {0} must not be confused.
Frequently asked questions
What is the correct answer to this question?
It is equal to {0}
Why is this the correct answer?
The empty set, written as ∅, contains no elements, so its cardinality is 0. It is also finite because a finite set has a limited number of elements, including zero elements. However, {0} is not empty: it contains the number 0 as one element and therefore has cardinality 1. Thus the statement that the empty set equals {0} is false. The symbols ∅ and {0} must not be confused.
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.
