Basic HTML Version
© 2014 Pacific Crest
71
2.2
Logical Reasoning
P
urpose
The role this topic plays in quantitative reasoning
Logical reasoning is the foundation of mathematical learning. Proofs or derivations are the logical
process of taking what is known or given as true premises and, through careful step-wise reasoning,
inferring interim results until the final result is determined and verified as true. Reasoning logically is
the ability to think through something rationally, deducing a conclusion from a set of logical steps. A
very basic example is:
if A > B and B > C then A > C
This form is a blend of English and mathematical symbols. Logical reasoning can also be presented
purely symbolically:
A > B
˄
B > C
→
A > C
or in plain English:
If Alice is older than Brendan and Brendan is older than Charlene, then Alice is older than Charlene.
Logical reasoning also includes the ability to recognize when errors are made as a result of accepting
false premises or making invalid inferences.
Reasoning logically means using logic in your thinking process, whether you’re working with something
relatively simple, such as truth tables, or the kinds of cosmic and eternal questions that philosophers
work with. Within the quantitative fields, the ability to think logically is highly valued and considered
one of the most important characteristic a person can have. The stronger your logical reasoning ability
becomes, the less likely it is that others will be able to influence your thinking with illogical and poorly
reasoned arguments.
L
earning Goals
What you should learn while completing this activity
1. Master the language of logic that includes basic logical operators and statements.
2. Expand your logical reasoning skills to include the validation of proofs and derivations.
3. Strengthen your ability to draft logically sound arguments.
D
iscovery
Finding out for yourself
Complete one of the following discovery exercises:
1. Enjoy playing with the logic puzzles available from the companion website. Try to solve three of
them. After working with the puzzles, what are three things you learned that improved your ability
to reason logically?