91Ó°ÊÓ

Let \(P(x)\) be the propositional function " \(x \geq x^{2}\)." Tell whether each proposition in Exercises \(16-24\) is true or false. The domain of discourse is \(\mathbf{R}.\) $$ P(2) $$

Given that proposition p is false, proposition q is true, and proposition risfalse, determine whether each proposition in is true or false. $$ p \vee q $$

Assuming that \(p\) and \(r\) are false and that \(q\) and \(s\) are true, find the truth value of each proposition. $$ (p \rightarrow q) \wedge(q \rightarrow r) $$

In Exercises \(15-19\), write the given argument in words and deter. mine whether each argument is valid. Let P: The for loop is faulty. q: The while loop is faulty. \(r:\) The hardware is unreliable. s: The output is correct. $$ \begin{array}{l} (p \rightarrow r) \rightarrow q \\ (q \rightarrow s) \rightarrow p \\ r \wedge s \\ p \vee q \\ \therefore p \wedge q \end{array} $$

Let \(P(x)\) be the propositional function " \(x \geq x^{2}\)." Tell whether each proposition in Exercises \(16-24\) is true or false. The domain of discourse is \(\mathbf{R}.\) $$ P(1 / 2) $$

Given that proposition p is false, proposition q is true, and proposition risfalse, determine whether each proposition in is true or false. $$ \neg p \vee \neg q $$

Assuming that \(p\) and \(r\) are false and that \(q\) and \(s\) are true, find the truth value of each proposition. $$ (p \rightarrow q) \rightarrow r $$

In Exercises \(15-19\), write the given argument in words and deter. mine whether each argument is valid. Let P: The for loop is faulty. q: The while loop is faulty. \(r:\) The hardware is unreliable. s: The output is correct. $$ \begin{array}{l} p \rightarrow q \\ q \rightarrow r \\ \neg r \\ s \rightarrow r \\ \hline \therefore \neg s= \end{array} $$

In Exercises \(15-19\), write the given argument in words and deter. mine whether each argument is valid. Let P: The for loop is faulty. q: The while loop is faulty. \(r:\) The hardware is unreliable. s: The output is correct. $$ \begin{array}{l} p \rightarrow(q \vee r) \\ q \rightarrow(p \vee s) \\ p \vee-q \\ \cdots s \\ \hline \therefore p \vee r \end{array} $$

Given that proposition p is false, proposition q is true, and proposition risfalse, determine whether each proposition in is true or false. $$ \neg p \vee q $$