## Proof Exercise #2 Continuation 2

Yes.

We will consider the square of the quantity (p - q). That is, (p - q)^2. This expression is necessarily non-negative.

Thus, we have the inequality, "0 is less than or equal to (p - q)^2".

What do you suggest, from the following list, for our next step to be?

choice #1: Interchange p and q in the inequality.

choice #2: Replace p with the smallest odd prime, and q with the next prime after that one.

choice #3: Consider p and q to be the legs of a right triangle.

choice #4: Replace (p - q)^2 in the inequality by its expansion.

choice #5: Replace (p - q)^2 in the inequality by (p - q)^4.

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We will consider the square of the quantity (p - q). That is, (p - q)^2. This expression is necessarily non-negative.

Thus, we have the inequality, "0 is less than or equal to (p - q)^2".

What do you suggest, from the following list, for our next step to be?

choice #1: Interchange p and q in the inequality.

choice #2: Replace p with the smallest odd prime, and q with the next prime after that one.

choice #3: Consider p and q to be the legs of a right triangle.

choice #4: Replace (p - q)^2 in the inequality by its expansion.

choice #5: Replace (p - q)^2 in the inequality by (p - q)^4.

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