(a) Prove that if n is an integer and 3n + 1 is odd, then 2n + 8 is divisible by 4....

(a) Prove that if n is an integer and 3n + 1 is odd, then 2n + 8 is divisible by 4.

(b) Assume a ≠ 3. Prove that if a is a solution to x² − x − 6 = 0, then a is a solution to x³ + 2x² + x + 3 = 0.

(c) Assume Prove that a is a solution to x² − x − 6 = 0 iff a is a solution to x³ + 2x² + x + 3 = 0.

(d) Let x be a real number. Prove that if x² = 2x + 15, then x ≤ 2 or

(e) Let x and y be real numbers. Prove that x + y if is irrational, then either x or y is irrational.

(f) Prove that if two nonvertical lines are perpendicular, then the product of their slopes is (Recall that nonvertical lines are those lines in the plane that have slope.)

(g) No point inside the circle (x − 3)² + y² = 6 is on the line y = x + 1.

(h) Prove that for all real numbers