Functions - Discrete Math

Hello;

I am looking for an explanation/guidance on how functions work. Here is what I have:

1.) Determine whethr each of the following relations is a function with domain {1,2,3,4}. For any relation that is not a function, explain why it isn't.

a.) f={1,1), (2,1), (3,1), (4,1), (3,3)}. - The answer in back of the book states the following: "Not a function; f contains two different pairs of the form (3,-)." What does the dash mean?

b.) f={(1,2), (2,3), (4,2)} - ?

d.) f={(1,1), (1,2), (1,3), (1,4) - ?

e.) f={(1,4), (2,3), (3,2), (4,1)} - ?

Re: Functions - Discrete Math

Quote:

Originally Posted by

**rtrumpow** Here is what I have: 1.) Determine whethr each of the following relations is a function with domain {1,2,3,4}. For any relation that is not a function, explain why it isn't.

a.) f={1,1), (2,1), (3,1), (4,1), (3,3)}. - The answer in back of the book states the following: "Not a function; f contains two different pairs of the form (3,-)." What does the dash mean?

b.) f={(1,2), (2,3), (4,2)} - ?

d.) f={(1,1), (1,2), (1,3), (1,4) - ?

e.) f={(1,4), (2,3), (3,2), (4,1)} - ?

By definition a relation on a set is a function if:

1) **Every element in the set in the first tern some pair in the relation.**

2) **No two pairs have the same first term.**

Now in (a) #2 is violated. HOW?

Now in (b) #1 is violated. HOW?

Please answer and complete,

Re: Functions - Discrete Math

#2 is in violation because of being the first term in two separate pairs.

#1 contains the same violation.

Re: Functions - Discrete Math

Quote:

Originally Posted by

**rtrumpow** #2 is in violation because of being the first term in two separate pairs. CORRECT!

#1 contains the same violation. INCORRECT

That is one out two.

What about the parts c) & d) ?