Discrete Math Determine and explain whether the function f

Discrete Math:

Determine and explain whether the function f : x is onto if

a. f(m,n) = m + n

b. f(m,n) = m - n

c. f(m,n) = m² + n²

Solution

Solution:

We know that a function to be \"onto,\" then every value in the set that it maps to has to appear in the set of values of the function

f to map onto Z, then every integer has to be a value of that function

If you plug in every integer for m and n

(a) f(m,n) = m + n is onto because

It will hit every integer. Again, if you pick any integer you want for m, you can cover the entire set just by running n through the whole set.

(b) f(m,n) = m-n is onto

Pick any value for m, and then use all the integers for n, and you will end up getting full coverage.

(c) f(m,n) = m^2 + n^2 is not onto

because  this will miss some integers. Because we are adding members of the set {0, 1, 4, 9, 16, 25, ...} from each other, we are going to miss a lot of integers in our result set.