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anonymous
 one year ago
Identify the following relation on ℕ as onetoone, onetomany, manytoone, or manytomany:
R = {(x,y)  x = y+1}
anonymous
 one year ago
Identify the following relation on ℕ as onetoone, onetomany, manytoone, or manytomany: R = {(x,y)  x = y+1}

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@zepdrix hey buddy, feel like helping me do a little math?

phi
 one year ago
Best ResponseYou've already chosen the best response.0if you know what number y is , can you find x ?

phi
 one year ago
Best ResponseYou've already chosen the best response.0if you know x, could you find y ?

phi
 one year ago
Best ResponseYou've already chosen the best response.0if you can do that, then it is onetoone.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, thank you. it wasn't put so simply in my text :X

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@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
 one year ago
Best ResponseYou've already chosen the best response.0do you know what f(1) means ?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, and do you know how to "evaluate" f(1) ? i.e. what number is that ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you plug it into all the x for f(x). so, i just plug 75 into both sides?

phi
 one year ago
Best ResponseYou've already chosen the best response.0f(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
 one year ago
Best ResponseYou've already chosen the best response.0(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) ?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, and that means g( f(75) )= g(5625) g(x) = 2x 3 what is g(5625)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so its left to right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it would have been different if i had done the other side first

phi
 one year ago
Best ResponseYou've already chosen the best response.0you 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)= 2x3 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
 one year ago
Best ResponseYou've already chosen the best response.0yes, there is no guarantee we get the same answer for (f∘g)(75)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you're sure about this?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, 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. \(x^2\)

phi
 one year ago
Best ResponseYou've already chosen the best response.0normally 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
 one year ago
Best ResponseYou've already chosen the best response.0Okay, 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
 one year ago
Best ResponseYou've already chosen the best response.0 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?

phi
 one year ago
Best ResponseYou've already chosen the best response.0a 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
 one year ago
Best ResponseYou've already chosen the best response.0so, this set isn't symmetric because you can put in x = 1 y = 2 but you cant put 2x and y = 1

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, exactly. it has (1,2) but not (2,1), so not symmetric
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