Which statement is correct?
Answer and explanation
Correct answer: Two equal sets have the same number of elements.
If two sets are equal, they contain exactly the same elements. Consequently, their cardinalities, or numbers of elements, must also be equal. However, the converse is not generally true: for example, {1, 2} and {a, b} have the same cardinality but are not equal because their elements differ. Also, ∅ has zero elements, while {0} has one element.
Frequently asked questions
What is the correct answer to this question?
Two equal sets have the same number of elements.
Why is this the correct answer?
If two sets are equal, they contain exactly the same elements. Consequently, their cardinalities, or numbers of elements, must also be equal. However, the converse is not generally true: for example, {1, 2} and {a, b} have the same cardinality but are not equal because their elements differ. Also, ∅ has zero elements, while {0} has one element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
