# Set Theroy

• Apr 8th 2008, 11:01 AM
Tom101
Set Theroy
Let D={2,3,4} and E={1,2,3} define the Funcation f: D->E by the rule
f(1)=1, f(2)=3, f(3)=1 and f(4)=2

a)What is the image of 3
b) what is the codonmain of f
c)draw the digraph representing f
d) is the funcation injective or subjectiv enad why

so i have done question similiar to this but i am totally stumped by this one do if any help would be much appricated and the more detailed the more i can learn form it

many many thanks

Tom
• Apr 8th 2008, 11:08 AM
Jhevon
Quote:

Originally Posted by Tom101
Let D={2,3,4} and E={1,2,3} define the Funcation f: D->E by the rule
f(1)=1, f(2)=3, f(3)=1 and f(4)=2

a)What is the image of 3

another way to phrase this question is: what does f(3) = ?

Quote:

b) what is the codonmain of f
if g:A -> B is a function. the domain is A and the codomain is B

you should look up the definitions of "domain" and "codomain"

Quote:

c)draw the disgraph representing f
what's a "disgraph"?

Quote:

d) is the funcation injective or subjectiv enad why
injective means one to one.

one to one means. If f(a) = f(b), then a = b, for all elements in the domain. So basically, if two images are the same, then the number in the domain that maps to them must be the same.

Hint: find two images that are the same, do they come from the same thing?

surjective means onto. this means that EVERY element in the codomain is mapped to, that is, every element in the codomain is the image of some element in the domain
• Apr 10th 2008, 05:00 AM
Tom101
thanks, i have done most of it now, a disgraph was a typo and i meant a digraph

many thanks
• Apr 10th 2008, 06:57 PM
Jhevon
Quote:

Originally Posted by Tom101
thanks, i have done most of it now, a disgraph was a typo and i meant a digraph

many thanks

still don't know what a digraph is. i will look it up if i have time, but you probably solved the problem already