Page 748 - Basic College Mathematics with Early Integers

724 A PPEND I X C I INDUCTIVE AND DEDUCTIVE REASONING

PRACTICE 3 Example 3 Find the next letter in each sequence.
Find the next letter in each
a. J, F, M,A, M
sequence.
b. A, E, D, H, G
a. S, M,T,W,T
b. A, F, D, I, G Solution:

a. Each letter is the first letter of some of the months of the year, in order:
January, February, March,April, May.The next month is June, so the letter is J.
b. Let’s look for a pattern by corresponding each letter of the alphabet to a num-
ber, according to order.
A E D H G
R Q R Q R Q R Q
1 + 4 = 5 5 - 1 = 4 4 + 4 = 8 8 - 1 = 7
Add 4 Subtract 1 Add 4 Subtract 1
From this pattern, the next letter is
G K
R Q
7 + 4 = 11
Work Practice 3

PRACTICE 4 Example 4 Use inductive reasoning to find the next shape in the sequence.
Use inductive reasoning to find
X X
the next possible shape in the
sequence. X
, ,
Solution: Notice that the “x” rotates clockwise in each square. Also, there is a
dot always diagonally across from each x. Thus, we might reason that the next
shape is the following.

X

Work Practice 4

Next, let’s study deductive reasoning.We begin with a definition.

Objective Using Deductive Reasoning

Deductive Reasoning

This is the process of forming a specific conclusion based on accepted assumptions.
leads to a
General Assumptions : specific conclusion

Copyright 2012 Pearson Education, Inc.
In short, with inductive reasoning, we reason from specific examples observed
to a general conclusion; with deductive reasoning, we reason logically from general
Answers
statements or assumptions to a specific conclusion.
3. a. F (each letter is the first letter of
the days of the week) b. L
4.