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Q
uantitative
R
easoning &
P
roblem
S
olving
80
© 2014 Pacific Crest
5. What is the implication of skipping a logical step and making an assumption instead?
6. How do you know that you have completed a line of logical reasoning?
7. What are the difficulties in using truth tables?
A
Successful Performance
Successful application of your learning looks like this
As you begin to apply what you’ve learned, you should have a good idea of what success looks like.
A SUCCESSFUL
PERFORMANCE
I d
emonstrate logical reasoning given a proof, derivation or logic problem. I...
●
Identify and correct fallacies
●
Justify the rationale (Why) for each step of a proof, derivation, or problem solution
●
Clearly explain unique conditions and issues of the context that causes variations in
the logical reasoning
D
emonstrate Your Understanding
Apply it and show you know in context!
1. Show that
A → B
is equivalent to
~B → ~A
by constructing truth tables for both and showing
the truth tables are equivalent. (Remember that the arrow used here, in the context of logic, is a
conditional if-then operator!)
2. Explain why the equivalence shown in problem 1 is a justification for proof by contradiction.
3. Use truth tables to show that each of the following arguments is incorrect.
a.
(A ˅ B) ˄ A→ ~B
b.
(A→ B) ˅ B →A
c.
(A→ B) ˅ ~A→ ~B