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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

Determine whether the argument is an example of inductive reasoning or deductive reasoning. The following equations show that n 2 n + 11 is a prime number for all counting numbers is = 1 , 2 , 3

,

4

,…

( 1 ) 2 1 + 11 = 11 n = 1

( 2 ) 2 2 + 11 = 13 n = 2

( 3 ) 2 3 + 11 = 17 n = 3

( 4 ) 2 4 + 11 = 23 n = 4

Note: A prime number is a counting number greater than 1 that has no counting number factors other than itself and 1 . The first 15 prime numbers are 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , and 47 .

To determine

Whether tile argument is an example of inductive reasoning or deductive reasoning.

The following equations show that n2n+11 is a prime number for all counting numbers n=1,2,3,4,...... .

  (1)21+11=11n=1(2)22+11=13  n=2(3)23+11=17    n=3(4)24+11=23    n=4

Explanation

Given Information:

  (1)21+11=11n=1(2)22+11=13  n=2(3)23+11=17    n=3

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