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Consider the statement that 3n – 2 is an odd number for all n = 1,2, 3, .... Which of the following statements is necessary to prove the statement via mathematical induction? I) Assume 3k – 2 is an odd number, then 3(k+1)-2 is also an odd number. II) Let n be arbitrary. Show that 3 * n – 2 is an odd number. III) Show that 3·1 – 2 is an odd number. IV) Pick two values of n at random and show that the statement is true for these chosen n values. Multiple choice: a) “I only" b) “II only" c) “III only" d) “IV only"

Consider the statement that 3n – 2 is an odd number for all n = 1,2, 3, .... Which of the following statements is necessary to prove the statement via mathematical induction? I) Assume 3k – 2 is an odd number, then 3(k+1)-2 is also an odd number. II) Let n be arbitrary. Show that 3 * n – 2 is an odd number. III) Show that 3·1 – 2 is an odd number. IV) Pick two values of n at random and show that the statement is true for these chosen n values. Multiple choice: a) “I only" b) “II only" c) “III only" d) “IV only"

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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Consider the statement that 3n – 2 is an odd number for all n = 1,2, 3, .... Which of the following statements is necessary to prove the statement via mathematical induction? I) Assume 3k - 2 is an odd number, then 3(k+1)– 2 is also an odd number. II) Let n be arbitrary. Show that 3 * n – 2 is an odd number. III) Show that 3.1- 2 is an odd number. IV) Pick two values of n at random and show that the statement is true for these chosen n values. Multiple choice: a) "I only" b) “II only" c) "III only" d) “IV only" e) "I and II only" f) "I and III only" g) "I and IV only" h) “II and III only" i) "II and IV only" k) "III and IV only"
Transcribed Image Text:Consider the statement that 3n – 2 is an odd number for all n = 1,2, 3, .... Which of the following statements is necessary to prove the statement via mathematical induction? I) Assume 3k - 2 is an odd number, then 3(k+1)– 2 is also an odd number. II) Let n be arbitrary. Show that 3 * n – 2 is an odd number. III) Show that 3.1- 2 is an odd number. IV) Pick two values of n at random and show that the statement is true for these chosen n values. Multiple choice: a) "I only" b) “II only" c) "III only" d) “IV only" e) "I and II only" f) "I and III only" g) "I and IV only" h) “II and III only" i) "II and IV only" k) "III and IV only"
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