1.5.7 Suppose a, b, c, and d are positive integers. Write a proof of each biconditional statement

Problem 1.5.7 From Smith/Eggen's A Transition to Advanced Mathematics 7th edition from chapter 1, logic and proofs - basic proof methods II.
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Suppose a, b, c, and d are positive integers. Write a proof of each biconditional
statement.
(a) ac divides bc if and only if a divides b.
(b) a +1 divides b and b divides b + 3 if and only if a = 2 and b = 3
(c) a is odd if and only if a + 1 is even.
(d) a + c = b and 2b - a = d if and only if a = b - c and b + c = d