Give an example of a function from the set of all integers to the set of all negative even integers that is onto, but not one-to-one. For the case of not one-to-one, give a counterexample. For the case of onto state briefly why you think the function is onto. You do not need to create a formal 2-column statement/justification proof that the function is onto. Piecewise functions are acceptable if properly defined.

Consider the function that assigns each positive integerto its FIRST (leading) digit. (For example, the positive integer 517 gets assigned to 5). In Blank 1: VWhat is the domain of this function? In Blank 2: What is the range of this function? (note I am not asking for the co- domain here) Please use either the roster method or set-builder notation for your response. In Blank 3: Is this function injective? (yes or no) Blank # 1 Blank # 2 Blank # 3

In this problem, assume that A and B are subsets of N, and f is a function N→ N. N-ACN. Write in terms of quantifiers over natural numbers (like the statement in the next part): Write in terms of set operations (like the statement in the previous part): Vn EN,n & A (ne B vn=1). Write in terms of quantifiers: f(A) SA.

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