CPE.251.FE.1.2023

In a proof by mathematical induction, what is the second step after proving the statement for n = 1?

• Assume the statement is true for some value of n

• Prove the statement for n = k

• Prove the statement for n = 2

• State the statement to be proved

What is mathematical induction used to prove?

• Geometrical theorems

• Algebraic equations

• Number theory results

• All of the choices

What type of statement is typically proven using mathematical induction?

• Conditional statements

• Universal statements

• Existential statements

• Biconditional statements

Mathematical induction is based on which principle?

• The principle of strong induction

• The principle of weak induction

• The principle of mathematical reasoning

• The principle of mathematical deduction

In the principle of mathematical induction, which of the following steps is mandatory?

• induction hypothesis

• inductive reference

• induction set assumption

• minimal set representation

For every natural number k, which of the following is true?

• m*k = n + 1

• (m+n)^k = k + 1

• m^kn = mn^k

• (mn)^k = m^kn^k

According to principle of mathematical induction, if P(k+1) = m^(k+1) + 5 is true then _____ must be true.

• P(k) = 3m^(k)

• P(k) = m^(k) + 5

• P(k) = m^(k+2) + 5

• P(k) = m^(k

Which of the following is the base case for 4ⁿ⁺¹ > (n+1)² where n = 2?

• 64 > 9

• 16 > 2

• 27 < 91

• 54 > 8

What is the induction hypothesis assumption for the inequality m! > 2^m where m>=4?

for m=k, k+1!>2^k holds

• for m=k, k+1!>2^k holds

• for m=k, k!>3^k holds

• for m=k, k!>2^k+1 holds

• for m=k, k!>2^k holds

Suppose that P_(n) is a propositional function. Determine for which positive integers n the statement P_(n) must be true if: P₍₁₎ is true; for all positive integers n, if P_(n) is true then P_(n+2) is true.

• P₍₃₎

• P₍₂₎

• P₍₄₎

• P₍₆₎