2. Which of the following can only be used in disproving the statements?a) Direct proofb) Contrapositive proofsc) Counter Exampled) Mathematical Induction

6. Use a direct proof to show that the sum of two odd integers is even.7. Use a direct proof to show that the sum of two even integers is even Show that if n is an integer andn3 + 5 is odd, then n is even usinga) a proof by contraposition.b) a proof by contradiction.8. Prove that if n is a positive integer, then n is odd if and only if 5n + 6 is odd.9. Find a counterexample to the statement that every positive integer can be written as the sum of thesquares of three integers.

When to proof P→Q true, we proof P false, that type of proof is known as ___________ ans. Direct proof Vacuous proof Contrapositive proofs Mathematical Induction

18) Why might a mathematician choose to use mathematical induction to prove a statement?a) To prove the statement for an infinite number of casesb) To find the roots of a polynomialc) To disprove a conjectured) To solve a system of equations

15) In mathematical induction, what is the purpose of the base case?a) To provide a general formulab) To disprove the given statementc) To provide a starting point for the inductiond) To solve for unknown variables

Which of the following statements about deductive and inductive arguments is correct?Question 6Select one:A.Some deductively invalid arguments give good reasons for accepting a conclusion.B.Inductive arguments are always deductively valid.C.Inductively strong arguments are always valid.D.Sound arguments always have either one or two premises.E.Inductive arguments are always persuasive.