Only need parts e and f ! Thanks

5. Prove the following statements using direct proof. (10 points each) Remember that this course is about learning how to read and write formal proofs! Use for definitions in your proofs including the formal definitions of odd and even numbers. Say "odd times odd is odd" is not sufficiently formal for our formal proofs! (a) If a is an odd integer, then a2+3a + 5 is odd. An example of an incorrect proof: Let a Then a2 +3a +5 32 +3.3+5 9+9+5-23, which is odd. This only verifies the result for a specific example of a. Our proof needs to show that it's true for all values of a 3, which is odd. (b) Suppose a, b, c e Z. If a2 lb and b3ic, then a c. Z, then n2 + 3n + 6 is even. (Prove it separately for the cases n even and 5x, then r If n (c) (d) Suppose z, y E R. If x2 + 5y (e) If a, beN with ged(a, b) >1, then bla or b is not prime. (f) If n is odd, then 81(n2 -1). y2 + y or c+y 5