Relations and Functions
Usual symbols for the above are;
Relations
To understand the symbolism better, let’s say the domain of a relation, R, is A = { a, b , c} and the Codomain is B = { 1,2,3,4}.
Here is the relation: a R 1, b R 4, b R 3, and c R 2.
We could also write (a,1) ε R, (b,4) ε R, (b, 3) ε R and (c,2) ε R.
Writing R as a set of ordered pairs, we have, R = { (a,1), (b,4,), (b,3), (c,2)}
Functions:
I will use a numerical function to illustrate symbolism used here, but remember a function, f, need not have any numbers in it.
Let’s say we have a function f that takes a number in its domain multiplies it by 2 and then subtracts 5. We might write f(x) = 2x – 5. Let’s also say that the domain of this function is A = { 1,2,3,4,5} and the Codomain is B = {5, 4, 3, 2, 1, 0, 1,2,3,4,5,6}. The Range is not the entire codomain.
Some ways of expression this function are the following:
1 f 3, 2 f 1, 3 f 1 and so on. This way is not the usual way, however.
The following are more standard ways:
f = {(1, 3), (2, 1), (3, 1), (4, 3), (5, 5) or we might write
(1, 3) ε f, (2, 1) ε f, (3,1) ε f, (4,3) ε f, and (5,5) ε f.
Or in a more familiar way you might write: f(1) = 3, f(2) = 1, f(3) = 1, f(4) = 3 and f(5) = 5.
You complete this table for 10 extra credit points
Send only these last three pages to me via email by the announced due date . The name of the file should be YourLastName_ section 4.1
State the Domain and Codomain. 
Express relationship for 4 ordered pairs 
Express the relationship using notation like a R b 
Is the relationship a function? If the answer is yes, explain why. If the answer is No, give me an example of a domain element going to more than one Codomain element. 
Give 4 ordered pairs in the inverse relationship. Two should be in the ordered pair notation and two in the R^{1} notation. 

This first row is just an example. The domain is the set of letters in the alphabet and the Codomain is the set of colors. The relation R means that a letter in the alphabet is the first letter in a color name. 
For the one to the left the domain is D = {all letters in alphabet} and the Codomain is G = {all colors}. 
(r,red) ε R, ( b, blue) ∈ R, (p, pink) ∈ R and (y, yellow) ∈ R 
r R red, p R pink g R green o R orange 
No, R is not a function since (b, black) and (b, blue) both ∈ R 
(pink,p) ∈ R^{1} (yellow, y) ∈ R^{1} Green R^{1} g Orange R^{1} o 
A number 1 – 26 is associated with the letter in the alphabet in that location. Use S for the relationship symbol here. 

A person is associated with his/her birth year. Use B as the relationship symbol 

State the Domain and Codomain. 
Express relationship for 4 ordered pairs 
Express the relationship using notation like a R b 
Is the relationship a function? If the answer is yes, explain why. If the answer is No, give me an example of a domain element going to more than one Codomain element. 
Give 4 ordered pairs in the inverse relationship. Two should be in the ordered pair notation and two in the R^{1} notation. 

A person is associated with his/her phone number. Use P for the relationship symbol 

A number is associated with its cube. Use C for the relationship symbol 

A number from N is associated with 0 if it is even and 1 if it is odd. Call the relationship R. 

A number from N is associated with its remainder when that number is divided by 3. Use M for the relationship symbol. 

State the Domain and Codomain. 
Express relationship for 4 ordered pairs 
Express the relationship using notation like a R b 
Is the relationship a function? If the answer is yes, explain why. If the answer is No, give me an example of a domain element going to more than one Codomain element. 
Give 4 ordered pairs in the inverse relationship. Two should be in the ordered pair notation and two in the R^{1} notation. 

A real number is associated with its reciprocal. Use L for the relationship symbol. 

A state in the US is associated with the year in which it was admitted to the Union. Use A for the symbol. 

A president of the US is associated with his/her order of presidency. Use P for the relationship. ASI type this file it is Nov 7 so I do not know if we will have our first female president or not. 
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