Question

Determine whether the function f:Z×Z→Z is onto if f(m,n)=m
a. True
b. False

Answer 1

The function f(m,n)=m is onto because every integer 'm' in the set of integers Z can be the output of the function, satisfying the condition for a function to be surjective.

Step-by-step explanation:

The student is asking whether the function f:Z×Z→Z defined by f(m,n)=m is onto (surjective). For a function to be onto, every element in the target set (in this case, the set of all integers Z) must be mapped by some pair in the domain set (Z×Z, which is the set of all pairs of integers). Since the function f(m,n) produces only the first element of the ordered pair, every integer 'm' in Z is an image under the function, regardless of the value of 'n'. Therefore, f is indeed an onto function because every integer in Z can be obtained by plugging in the appropriate 'm' value, regardless of 'n'. Consequently, the answer to the question is a. True