Chapter 3 Logical Formulas62
QWWDYou do every exercise in the book.RWWDYou get an A in the class.
Translate following assertions into propositional formulas usingP,Q,Rand
the propositional connectivesAND;NOT;IMPLIES.
(a)You get an A in the class, but you do not do every exercise in the book.(b)You get an A on the final, you do every exercise in the book, and you get an A
in the class.
(c)To get an A in the class, it is necessary for you to get an A on the final.(d)You get an A on the final, but you don’t do every exercise in this book; never-
theless, you get an A in this class.
Class Problems
Problem 3.3.
When the mathematician says to his student, “If a function is not continuous, then it
is not differentiable,” then lettingDstand for “differentiable” andCfor continuous,
the only proper translation of the mathematician’s statement would be
NOT.C/ IMPLIES NOT.D/;or equivalently,
D IMPLIES C:
But when a mother says to her son, “If you don’t do your homework, then you
can’t watch TV,” then lettingT stand for “can watch TV” andHfor “do your
homework,” a reasonable translation of the mother’s statement would be
NOT.H/IFF NOT.T/;