OpenStudy (anonymous):

Identify the following relation on ℕ as one-to-one, one-to-many, many-to-one, or many-to-many: R = {(1,3), (3,3), (3,1), (2,2), (2,3), (1,1), (1,2)} One-to-one One-to-many Many-to-one Many-to-many

2 years ago
OpenStudy (anonymous):

I'm looking through definitions of all these things now. If anyone wants to help explain "one-to-one, one-to-many, many-to-one, and many-to-many" while I research that would be awesome :)

2 years ago
zepdrix (zepdrix):

Example of One-to-one: S={ (1,2), (3,5), (4,7) } This is showing that `1 is in relation to 2` `3 is in relation to 5` `4 is in relation to 7` Example of One-to-many: S={ (1,2), (1,3), (4,6), (4,7), (5,9) } This is showing that `1 is in relation to 2 and 3` so this single element is mapped to many values `4 is in relation to 6 and 7` again this one element 4 is mapped to many values `5 is in relation to 9` Example of Many-to-one: S={ (1,2), (3,2), (4,2), (5,2), (6,7) } This is showing that `1 is in relation to 2` `3 is in relation to 2` `4 is in relation to 2` `5 is in relation to 2` Collectively, these are all showing us that many elements are mapped to 2. `6 is in relation to 7`

2 years ago
zepdrix (zepdrix):

Example of Many-to-many: S={ (1,2), (1,3), (2,3) } This is showing that `1 is in relation to 2 and 3` This one element 1 is being mapped to many values `1 is in relation to 3` `2 is in relation to 3` Collectively, these are showing us that many values are mapped to this one element 3

2 years ago
zepdrix (zepdrix):

So I guess umm... We would say that a relation is `Many-to-many` if it is both `Many-to-one` and `One-to-many`.

2 years ago
OpenStudy (directrix):

Many to Many is correct. @zepdrix "Many" x to the same y. (1 is mapped to 3, 2, and 1) "Many" y to the same x. (2 is mapped to 1 and 2)

2 years ago
OpenStudy (anonymous):

@Zepdrix Thanks man. How have you been?

2 years ago
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