Prove that for all real numbers a and b 2. negate the following statements (a) there exists a rational number q such that for all positive real mumbers ax,2 0 and ys = 43 3. prove that for all real numbers a, b, and c, we have be+ ac+aba2 + b? + c2. 4. let x and y be integers. prove that if is even and y is odd then x +y is odd. and y such that 2- y = 1 5. show that there are no natural numbers 6. using a proof by cases, show that, for all real numbers a and b la lalbl