True or false? Induction is a kind of thinking you use to form general ideas and rules based on mathematical formulas.A.TrueB.FalseSUBMITarrow_backPREVIOUS

You start with a given set of rules and conditions and determine something to be true. What type of reasoning did you use?A.deductiveB.logicalC.conditionalD.inductiveSUBMITarrow_backPREVIOUS

Assume that N = {0, 1, 2, 3, . . .}.(a) Suppose that we change the induction mechanism as follows:• Base case: Prove that P (0) is true• Inductive step: Prove that for all k ≥ 0, P (k) ⇒ P (k + 2)Explain why this would not constitute a valid proof that P (n) is true for alln ∈ N. How would you change the base case to obtain a valid proof?

16) What is proven in the inductive step of mathematical induction?a) The statement holds for all real numbers.b) The statement holds for an arbitrary case.c) The statement holds for the next case, given it holds for a particular case.d) The statement holds for the base case.

When to proof P→Q true, we proof P false, that type of proof is known as ___________ans.Direct proofMathematical InductionContrapositive proofsVacuous proof

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