Relations...

[jai]

Hello. I have this wierd looking problem. I have to state whether each relations of S is one to one, one to many, many to one, or many to many.

A) S = N [all natural num]
x rho y <-> x = y+1
B) S = set of all women in Vicksburg
x rho y <-> x is the daughter of y
C) S = the power set {1,2,3}
A rho B <-> |A| = |B|
D) S = R [all reals]
x rho y <-> x = 5

I know how to do this with numbers. Like with A, I think that would be many to many because the first component in the set can combine with more than one second component for x = y+1 to be true, and vice versa. But with the others, I am not so sure.

If any one could save me. . .

 

[pka]

this wierd looking problem. state whether each relations of S is one to one, one to many, many to one, or many to many.
A) S = N [all natural num]
x rho y <-> x = y+1
B) S = set of all women in Vicksburg
x rho y <-> x is the daughter of y
C) S = the power set {1,2,3}
A rho B <-> |A| = |B|
D) S = R [all reals]
x rho y <-> x = 5

I taught the foundations of mathematics courses for many years, but I have never seen these terms applied to relations that are not functions.
Can you confirm the correction definitions?
one-to-one not two pairs have the same first or the same last term.
one-to-many pairs have the same first term but different last terms.
many-to-one several pairs have the same last term.
many-to-many several pairs have the same first or last term.
Are these what your text means?

If so; A is one-to-one; B is many-to-one; C is many-to-many; D is one-to-many.

 

[jai]

Yeah, those are right. Thanks for your help!