EXAMPLE 2.2.5
Given:
i. If my car doesn't start, then I'll be late for work; and
ii. I'm not late for work.
select the statement that is a valid conclusion, if a valid conclusion is warranted.
A. My car started.
B. I rode the bus.
C. I'm late for work.
D. None of these is warranted.
SOLUTION

Let p be the statement "My car doesn't start."
Let q be the statement "I'm late for work."
The the premise arrangement has this form:

p arrow q.

Not q.


Note that this is the premise arrangement for a valid argument (Contrapositive Reasoning). We know that “not p” will be a valid conclusion. Thus, the correct choice is A.