1. (10 points) Prove the following statement without using a proof by contradiction: For all integers p, if p>1 and p3 is prime, then p is odd (20 points) Prove the following statement using a direct proof: For all rational numbers x and y, if y=0, then yx is rational. 3. (20 points) Prove the following statement using a proof by contradiction: You must also use the statement from Question 2, somewhere in your proof of the statement for this problem, in a natural and correct way. You must explicitly reference Question 2. You must also explicitly state the contradiction that you eventually reach. You may assume that the statement in Question 2 is true, even if you didn't prove it. You may also assume the standard properties of exponents, where, for any positive real numbers b,c and any real numbers x and y, the following equalities are always true: 1. bx=0 2. bxby=bx+y 3. (bx)y=bxy 4. bvb2=bxy 5. (bc)x=bxcx DO NOT just mimic the proof that we did in class of the fact that 2 is not rational. There is a simpler approach