Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 67 — #75
3.7. References 67
Translate following assertions into propositional formulas using P , Q, R and
the propositional connectives AND; 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; nevertheless,
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 letting D stand for “differentiable” and C for 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 letting T stand for “can watch TV” and H for “do your
homework,” a reasonable translation of the mother’s statement would be
NOT.H / IFF NOT.T /;
or equivalently,
H IFF T: