anonymous
  • anonymous
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}
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
@zepdrix hey buddy, feel like helping me do a little math?
phi
  • phi
if you know what number y is , can you find x ?
anonymous
  • anonymous
yes

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phi
  • phi
if you know x, could you find y ?
anonymous
  • anonymous
yes
phi
  • phi
if you can do that, then it is one-to-one.
anonymous
  • anonymous
okay, thank you. it wasn't put so simply in my text :X
anonymous
  • anonymous
@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?
phi
  • phi
do you know what f(1) means ?
anonymous
  • anonymous
that f(x)=f(1)
phi
  • phi
yes, and do you know how to "evaluate" f(1) ? i.e. what number is that ?
anonymous
  • anonymous
you plug it into all the x for f(x). so, i just plug 75 into both sides?
phi
  • phi
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
phi
  • phi
(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) ?
anonymous
  • anonymous
5625
phi
  • phi
yes, and that means g( f(75) )= g(5625) g(x) = 2x -3 what is g(5625)
anonymous
  • anonymous
11247
phi
  • phi
that is how you do it.
anonymous
  • anonymous
so its left to right?
anonymous
  • anonymous
it would have been different if i had done the other side first
phi
  • phi
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
phi
  • phi
yes, there is no guarantee we get the same answer for (f∘g)(75)
anonymous
  • anonymous
you're sure about this?
phi
  • phi
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. \(x^2\)
anonymous
  • anonymous
its ^2
phi
  • phi
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
 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?
anonymous
  • anonymous
phi
  • phi
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"
anonymous
  • anonymous
so, this set isn't symmetric because you can put in x = 1 y = 2 but you cant put 2-x and y = 1
phi
  • phi
yes, exactly. it has (1,2) but not (2,1), so not symmetric

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