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.