Suppose x is a real number. Prove that if x 1 then there is a real number y such that y+1 = x. 4-2

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Question 7. Express the following statement using the logic symbols, and decide whether it is true or false. Explain your answer briefly. The equation z² + y² = 1 has a solution (x, y) in which both z and y are natural numbers.

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Question 2. Express each statement in plain English. Then decide if the statement is true or false (including a brief explanation). Both x and y represent real numbers. (1) \xy(x² + y² ≤ 4) (2) \x³y(x² + y² ≤ 4) (3) ³xVy(x² + y² ≤ 4)

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Please help and explain how I would solve this in a proof form. Thank you in advance.Suppose a, b, and c are real numbers and a > b  and c<0.  Use the order properties in Section 2.2 of our Introduction to Analysis by Maxwell Rosenlicht to prove  ac < bc.