Exercises for self study. Complete these exercises in the textbook and
compare your solutions against those in the back of the book. These exercises
will not be graded.
pp. 14–16, Exercises 11 and 33
p. 38, Exercises 11 and 15
Exercises to be graded. Complete these exercises and turn in your
solutions.
State the converse and contrapositive of the conditional statement
“Trinity wins whenever it is sunny in Hartford.”
Using the propositions
$p =$ “I study,”
$q =$ “I will pass the course,” and
$r =$ “The professor is generous,”
translate the following into propositions of $p$, $q$, $r$ and logical
connectives, including negations:
(a) If the professor is generous, then I do not study.
(b) I will pass the course only if I study.
(c) The professor is not generous, but I study and will pass the
course.
(d) If I study, then the professor is generous and I will pass the
course.
(e) I will not pass the course, but the professor is generous.
Using only the logical connectives $\neg$, $\vee$ and $\wedge$, write a
proposition of $p$ and $q$ that is true if and only if exactly one of $p$
and $q$ is true. Prove correctness using a truth table.
Using only the identity, commutative, distributive and/or negation laws,
prove that $(p \wedge q) \vee (\neg p \wedge \neg q) \equiv
(p \vee \neg q) \wedge (\neg p \vee q)$ by a step-by-step series of logical
equivalences in which one such law is applied at each step.
Plagiarism and academic dishonesty.
Remember, under any circumstance, you must not copy part or all of another's
work and present it as your own. For more details, read
our course policy on plagiarism and
academic dishonesty.
