Question

Identify the following relation on ℕ as one-to-one, one-to-many, many-to-one, or many-to-many:

R = {(x,y) | x = y+1}

Answer 1

@zepdrix hey buddy, feel like helping me do a little math?

Answer 2

if you know what number y is , can you find x ?

Answer 3

yes

Answer 4

if you know x, could you find y ?

Answer 5

yes

Answer 6

if you can do that, then it is one-to-one.

Answer 7

okay, thank you. it wasn't put so simply in my text :X

Answer 8

@phi Calculate the following composition function using the functions f and g defined below:

f:N→N, f(x) = x2 and g:N→N, g(x) = 2x - 3

(g∘f)(75)

would you also mind showing me how to solve this kind of problem, please? does this mean that f(x) and g(x) = 75?

Answer 9

do you know what f(1) means ?

Answer 10

that f(x)=f(1)

Answer 11

yes, and do you know how to "evaluate" f(1) ? i.e. what number is that ?

Answer 12

you plug it into all the x for f(x). so, i just plug 75 into both sides?

Answer 13

f(x) is the "name"
\(x^2\) (I assume you mean this and not x*2)
is the "rule" or instruction

If we say f(x) we are using a "short name" for x^2
if we say f(1), that means replace x with 1 in the formula: we get 1^2 = 1*1= 1

Answer 14

(g∘f)(75)

is just ugly syntax that means
g( f(75) )

which is also a bit ugly.

but we tackle it in steps
for example, what is
f(75) ?

Answer 15

5625

Answer 16

yes, and that means
g( f(75) )= g(5625)

g(x) = 2x -3
what is g(5625)

Answer 17

11247

Answer 18

that is how you do it.

Answer 19

so its left to right?

Answer 20

it would have been different if i had done the other side first

Answer 21

you can also do this
(g∘f)(75)
first do (g∘f)(x) which means
g( f(x) )
that means replace x in the formula for g with f(x)
g(x)= 2x-3
g( f(x) )= 2* f(x) -3
but f(x) is x^2 so we get
g(f(x))= 2*x^2 -3
now we can do
(g∘f)(75) = 2*(75)^2 -3

Answer 22

yes, there is no guarantee we get the same answer for
(f∘g)(75)

Answer 23

you're sure about this?

Answer 24

yes, the process is correct. I am not sure what you mean by f(x)=x2
that might mean x^2 or x*2, but you will have to say which you meant. (x2 is not "legal" but lots of people don't know how else to write x^2 i.e. \(x^2\)

Answer 25

its ^2

Answer 26

normally people don't pick big numbers for x (like 75) because you get huge numbers, and the point is not to learn arithmetic, but how to compose functions.

Answer 27

Okay, that is pretty straight forward. I was just confused about what the symbol meant and which came first; or, if i was going to get two answers. I have one other things i need to clear up and that is determining weather sets are reflexive, symmetric, transitive, or asymetric.

You did a pretty great job explaining 1 to 1 earlier. I wonder if you can help me out with a couple other questions.

 Symmetric: For every element x or y in the set, if (x,y) is in the
relation then (y,x) is also in the relation.

 Antisymmetric: For every element x or y in the set, for every case where
(x,y) and (y,x) are both in the relation, x = y.

 Reflexive: For every element x in the set, (x,x) is in the relation.

 Transitive: For every set of three elements x, y, and z, if (x,y) and
(y,z) are in the relation then (x,z) is also in the relation.

^^ these are my definitions

Let S = {1,2,3}. Determine the truth value of the statement:
The following relation is symmetric on S.
R1 = {(1,3), (3,3), (3,1), (2,2), (2,3), (1,1), (1,2)}

and that is my problem.

Answer 28

 Symmetric: For every element x or y in the set, if (x,y) is in the
relation then (y,x) is also in the relation. i actually do not understand what this means. if the x,y is in relation that means it's in an ordered pair, right?

Answer 29

@phi

Answer 30

a relation has an "in" and an "out"
you start with x (the input) , and use a formula to find y (the output)
(x,y) means we put in "x" and got out "y"
(y,x) means we put in "y" and got out "x"

Answer 31

so, this set isn't symmetric because you can put in x = 1 y = 2 but you cant put 2-x and y = 1

Answer 32

yes, exactly. it has (1,2) but not (2,1), so not symmetric