2.3.0: Exercises — Read — Invisible Network

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For the following exercises, find the truth value of each statement.

Exercise \(\PageIndex{1}\)

\(p: 7 \times 3=21\). What is the truth value of \(\sim p\) ?

Exercise \(\PageIndex{2}\)

\(q\) : The sun revolves around the Earth. What is the truth value of \(\sim q\) ?

Exercise \(\PageIndex{3}\)

\(\sim r\) : The acceleration of gravity is \(9.81 \mathrm{~m} / \mathrm{sec}^2\). What is the truth value of \(r\) ?

Exercise \(\PageIndex{4}\)

\(s\) : Dan Brown is not the author of the book, The Davinci Code. What is the truth value of \(\sim(\sim s)\) ?

Exercise \(\PageIndex{5}\)

\(t\) : Broccoli is a vegetable. What is the truth value of \(\sim(\sim t)\) ?

For the following exercises, given \(p: 1+2=3, q\) : Five is an even number, and \(r\) : Seven is a prime number, find the truth value of each of the following statements.

Exercise \(\PageIndex{6}\)

\(\sim q\)

Exercise \(\PageIndex{7}\)

\(p \wedge q\)

Exercise \(\PageIndex{8}\)

\(p \vee q\)

Exercise \(\PageIndex{9}\)

\(\sim p \vee \sim q\)

Exercise \(\PageIndex{10}\)

\(p \wedge \sim q\)

Exercise \(\PageIndex{11}\)

\(p \wedge r\)

Exercise \(\PageIndex{12}\)

\(q \wedge r\)

Exercise \(\PageIndex{13}\)

\(q \wedge \sim r\)

Exercise \(\PageIndex{14}\)

\(q \vee \sim r\)

Exercise \(\PageIndex{15}\)

\(\sim(p \wedge r)\)

Exercise \(\PageIndex{16}\)

\(p \vee q \wedge r\)

Exercise \(\PageIndex{17}\)

\(\sim p \vee(q \wedge r)\)

Exercise \(\PageIndex{18}\)

\(\sim(q \wedge r) \vee \sim p\)

Exercise \(\PageIndex{19}\)

\(q \vee r \vee p\)

Exercise \(\PageIndex{20}\)

\(\sim q \wedge r \wedge p\)

For the following exercises, complete the truth table to determine the truth value of the proposition in the last column.

Exercise \(\PageIndex{21}\)

\(p\)	\(q\)	\(r\)	\(\sim p\)	\(\sim p \vee q\)	\((\sim p \vee q) \wedge r\)
T	T	T

Exercise \(\PageIndex{22}\)

\(p\)	\(q\)	\(r\)	\(\sim p\)	\(\sim p \vee q\)	\((\sim p \vee q) \wedge r\)
F	T	F

Exercise \(\PageIndex{23}\)

\(p\)	\(q\)	\(r\)	\(\sim p\)	\(\sim r\)	\(\sim p \wedge q(\sim p \wedge q) \vee \sim r\)
F	F	F

Exercise \(\PageIndex{24}\)

\(p\)	\(q\)	\(r\)	\(\sim p\)	\(\sim r\)	\(\sim p \vee q\)	\((\sim p \vee q) \vee \sim r\)
F	F	F

For the following exercises, given \(p\) : All triangles have three sides, \(q\) : Some rectangles are not square, and \(r\) : A pentagon has eight sides, determine the truth value of each compound statement by constructing a truth table.

Exercise \(\PageIndex{25}\)

\(\sim r \wedge q \wedge p\)

Exercise \(\PageIndex{26}\)

\(\sim(q \wedge p) \vee r\)

Exercise \(\PageIndex{27}\)

\(\sim p \vee q \wedge r\)

Exercise \(\PageIndex{28}\)

\(\sim p \vee \sim q \vee r\) For the following exercises, construct a truth table to analyze all the possible outcomes for the following arguments.

Exercise \(\PageIndex{29}\)

\(\sim q \wedge q\)

Exercise \(\PageIndex{30}\)