If A and B are equal sets, which conclusion is necessary?
Answer and explanation
Correct answer: A and B have the same number of elements
Two sets are equal when they contain exactly the same elements, regardless of the order or notation used to write them. Therefore, whenever A = B, their cardinalities must also be equal; they have the same number of elements. However, equal sets may be finite, infinite, or empty, and they need not be written in the same form. Thus option A is necessary.
Frequently asked questions
What is the correct answer to this question?
A and B have the same number of elements
Why is this the correct answer?
Two sets are equal when they contain exactly the same elements, regardless of the order or notation used to write them. Therefore, whenever A = B, their cardinalities must also be equal; they have the same number of elements. However, equal sets may be finite, infinite, or empty, and they need not be written in the same form. Thus option A is necessary.
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.
