Prove that if a and b are positive integers whose sum is a prime p, their greatest common divisor is 1.

Proof by contadiction.

Let assume there exist such positive integers and whose sum is a prime number , that their greatest common divisor is greater than 1.

Since is a prime number and , then , but we assumed earlier that , and there are no two positive integers that sum up to 1.

q.e.d.

answer: the first graph

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.