Using the definition of divides, prove the following stateme…

Using the definition of divides, prove the following statement or provide a counterexample to disprove: “For all a, b, c ∈ ℤ with a ≠ 0, if a|b and a|c then a|(b + c).”  Use good proof technique.  Note:  To avoid the need to type special symbols, use ‘does not equal’ for ≠. Grading rubric: 1 pt. State the definition of divides at the beginning. 1 pt. State any givens and assumptions.  1 pt. Clearly explain your steps and reasoning. 1 pt. State the final conclusion at the end of the proof.

Prove, or provide a counterexample to disprove, the followin…

Prove, or provide a counterexample to disprove, the following statement:             “The function f : ℕ ⟶ ℕ  be defined by f(n) = n(mod 5) is onto.” Use good proof technique. Grading rubric:1 pt. State the definition of onto at the beginning, then prove or disprove.1 pt. State any givens and assumptions.1 pt. Clearly explain your reasoning.1 pt. Remember to state the final conclusion at the end of the proof.