 # Discrete Math Problems

## Question

(11a) Define g: Z -> Z by the rule g(n) = 4n-5 for all integers n.

(i) is g one to one? prove or give coutnerexample
(ii) is g onto? prove or give counterexample.

Use the following definition: If f: R->R and g: R->R are functions, then the function (f+g): R->R is defined by the formula (f+g)(x)=f(x)+g(x) for all real numbers x.

(31)
If f: R->R and g: R->R are both onto, is f+g also onto? Justify.

(8)
Define L:Z->Z and M:Z->Z by the rules L(a)=a^2 and M(a) = amod5 for all integers a.

(b) Is L o M = M o L ?

(18)
If f: X -> Y and g: Y -> Z are function and g o f is one to one, must f be one-to-one? prove or give counterexample.

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