Letaandbbe integers andda positive integer.(a) Prove that ifddividesaandddividesb, thenddivides botha+banda−b.(b) Is the converse of the above true? If so, prove it. If not, give a specific example ofa, b, dshowingthat the converse is false.

See step by step explanation.

Step-by-step explanation:

Recall that given two integers a, b, a divides b if there exists an integer k such that b = ka.

Let a,b,d be integers, such that d>0.

a) Suppose that d divides a and d divides b. Then, there exists such that and . Consider a+b and a-b. Replacing the previous equation, we have that

Since then and are both integers. Then, d divides both a+b and a-b.

b) It is false. Let a = 7, b = 5. Then d = 2 divides a+b (12) and a-b (2) but neither 2 divides 7 nor 2 divides 5.

Step-by-step explanation:

is one that can be written in the form. f (t) = A cos(Lt − f). (1) The function f (t) is a cosine function which has been amplified by A, shifted by f/L, and compressed by L. hope this helps!!