Question

The sets A and B have the same cardinality if and only if there is an onto correspondence from A to B.

true or false

Answer 1

False. An onto correspondence from A to B is not sufficient to conclude that A and B have the same cardinality.

Step-by-step explanation:

False. The sets A and B have the same cardinality if and only if there is a bijection (one-to-one and onto correspondence) between them. In other words, if every element in A is paired with a unique element in B and every element in B is paired with a unique element in A, then the sets have the same cardinality. An onto correspondence from A to B means that every element in B is paired with at least one element in A, but it doesn't guarantee a one-to-one pairing. Therefore, an onto correspondence alone is not sufficient to conclude that A and B have the same cardinality..