Please answer and explain. Thank you.

Show that product of two even integers is even by using a direct proof. Question 2 (10 points) Use a proof by contraposition to show that if x is a negative number, then x1 is negative. Question 3 (10 points) Give a proof by contradiction of the conjecture that if x is an even integer, then x+1 is odd. Question 4 (10 points) Use a proof by case to show that for every real number x, we have xx. Question 5 (10 points) Prove that if x is a positive integer, then x2+x3=50. Question 6 (10 points) Prove or disprove that there are no positive integer solutions for the equation 2x2+y2=10. Question 7 (10 points) Prove the conjecture about the real numbers x and y that x2=y2 if and only if x=y or x=y