EXAMPLE 2.2.8 SOLUTION
Let p be the statement "You want a better grade."
Let q be the statement "You bring an apple for the teacher."
Let r be the statement "You expose the teacher to dangerous agricultural
chemicals."
The premise arrangement has this form:
p arrow
q.
q arrow
r.
We see that this is the arrangement of premises for Transitive Reasoning, which is a form of valid reasoning. This means that we will be
able to form a valid conclusion, namely:
p arrow
r.
In words, the valid conclusion is "If you want a better grade, then you
expose the teacher to dangerous agricultural chemicals."
Unfortunately, this isn't one of the listed choices. We may now refer to the
following fundamental fact: If we have a statement that is a valid
conclusion for an argument, then any equivalent statement will also be a valid
conclusion.
In this particular case, the statement is a valid conclusion, so its equivalent
contrapositive will
also be a valid conclusion. Im words, the contrapositive of "If you want a better grade, then
you expose the teacher to dangerous agricultural chemicals," will also be
a valid conclusion. This is the statement "If you don't expose the teacher
to dangerous agricultural chemicals, then you don't want a better grade."
The correct choice is B.