# Functions - Discrete Math

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• Mar 18th 2013, 05:50 AM
rtrumpow
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)} - ?
• Mar 18th 2013, 06:13 AM
Plato
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,
• Mar 18th 2013, 09:11 AM
rtrumpow
Re: Functions - Discrete Math
#2 is in violation because of being the first term in two separate pairs.
#1 contains the same violation.
• Mar 18th 2013, 09:15 AM
Plato
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) ?