Section 1.1 & 1.2 Review Solutions

Select problems from the text (© McGraw Hill)

†The questions presented here have been adapted from Kenneth Rosen’s Discrete Mathematics and Its Applications, 8th Edition.

Problem 1 ¶

Let $p$ be the proposition “I will do every exercise in the textbook” and $q$ be the proposition “I will get an A in CS0441”.

Express each of these as a combination of $p$ and $q$.

a) I will get an A in CS0441 only if I do every exercise in the textbook.

b) I will get an A in CS0441 and I will do every exercise in the textbook.

c) Either I will not get an A in CS0441 or I will not do every exercise in the textbook.

Problem 2 ¶

Express your answer in terms of $e$: “You can edit a protected Wikipedia entry” and $a$: “You are an administrator”. You cannot edit a protected Wikipedia entry unless you are an administrator.

Problem 3 ¶

Express your answer in terms of $g$: “You can graduate,” $m$: “You owe money to the university,” $r$: “You have completed the requirements of your major,” and $b$: “You have an overdue library book”. “You can graduate only if you have completed the requirements of your major and you do not owe money to the university and you do not have an overdue library book.”

Problem 4 ¶

Show that these statements are inconsistent: “If Miranda does not take a course in discrete mathematics, then she will not graduate.”

“If Miranda does not graduate, then she is not qualified for the job.”

“If Miranda reads this book, then she is qualified for the job.”

“Miranda does not take a course in discrete mathematics but she reads this book.”

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