2n2 – 4n + 1 is even → n is odd

Show that [P (QV R)] → [(P → R) V (P Q)] is a tautology Question 5 using a truth table.

1. Find the contrapositive, converse and negation of the following statement. (Va € N) (Vb ≤ Z) (a² − b² > 0 ⇒ (a ≤ b) V (a + b ≤ N)) Contrapositive: • Converse: • Negation:

Provide formal proofs or disproofs of the following arguments (using predicate logic and truth-functional statements with Rules of Inference in Math Logic) for the following problem: "If anyone puts Ketchup in the soup, then the soup will be spoiled. If it is spoiled, then someone will be furious with John. No one is furious with John. Therefore, John did not put Ketchup in the soup."