1.Suppose a, b, c, and d are integers. Prove that if a|b and c|d, then (ac)|(bd).2. Let X be an integer. Prove that X is odd if and only if x+1 is even.3. Disprove:If a and b are non negative integers with a|b, then a≤b.Note: A counterexample to this statement would also be a counterexample for the previous problem, but not necessarily vice versa.4. Disprove: If a,b,and c are positive integers with a|(bc), then a|b or a|c.