Write the given argument in words and determine whether each argument is valid. Let p: 4 gigabytes is better than no memory at all, q: We will buy more memory, r: We will buy a new computer.

$$\begin{array}{l} p\rightarrow r \\ r\rightarrow q \\ p \\ \hline \therefore q \end{array}$$

Write the given argument in words and determine whether each argument is valid. Let p: 4 gigabytes is better than no memory at all, q: We will buy more memory, r: We will buy a new computer.

$$\begin{array}{l} p\rightarrow r \\ p\rightarrow q \\ \hline \therefore p\rightarrow (r\wedge q) \end{array}$$

Write the given argument in words and determine 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.

$$\begin{array}{l} (p\rightarrow r)\rightarrow q \\ (q\rightarrow s)\rightarrow p \\ r\wedge s \\ p\vee q \\ \hline \therefore p\wedge q \end{array}$$

Write the given argument in words and determine 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.

$$\begin{array}{l} p\rightarrow (q\vee r) \\ q\rightarrow (p\vee s) \\ p\vee \neg q \\ \neg s \\ \hline \therefore p\vee r \end{array}$$

Write the given argument in words and determine 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.

$$\begin{array}{l} (p\vee q)\rightarrow (r\vee s) \\ p \\ \neg r \\ \hline \therefore q \end{array}$$

Write the given argument in words and determine 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.

$$\begin{array}{l} (r\vee s)\rightarrow p \\ s\rightarrow q \\ p\vee s \\ \hline r \end{array}$$

Write the given argument in words and determine 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.

$$\begin{array}{l} p\rightarrow q \\ q\rightarrow r \\ \neg r \\ s\rightarrow r \\ \hline \therefore \neg s \end{array}$$

Formulate the arguments symbolically and determine whether each is valid. Let p: I study hard, q: I get A's, r: I get rich.

$$\begin{array}{l} \text{If I study hard or I get rich, then I get A's.} \\ \text{I get A's.} \\ \hline \therefore \text{If I don't study hard, then I get rich.} \end{array}$$

Formulate the arguments symbolically and determine whether each is valid. Let p: I study hard, q: I get A's, r: I get rich.

$$\begin{array}{l} \text{If I study hard, then I get A's.} \\ \text{I study hard.} \\ \hline \therefore \text{I get A's.} \end{array}$$

Formulate the arguments symbolically and determine whether each is valid. Let p: I study hard, q: I get A's, r: I get rich.

$$\begin{array}{l} \text{If I study hard, then I get A's or I get rich.} \\ \text{I don't get A's and I don't get rich.} \\ \hline \therefore \text{I don't study hard.} \end{array}$$

Formulate the arguments symbolically and determine whether each is valid. Let p: I study hard, q: I get A's, r: I get rich.

$$\begin{array}{l} \text{I study hard if and only if I get rich.} \\ \text{I get rich.} \\ \hline \therefore \text{I study hard.} \end{array}$$

Formulate the arguments symbolically and determine whether each is valid. Let p: I study hard, q: I get A's, r: I get rich.

$$\begin{array}{l} \text{If I study hard, then I get A's.} \\ \text{If I don't get rich, then I don't get A's.} \\ \hline \therefore \text{I get rich.} \end{array}$$

Formulate the symbolic expression in words using p: Today is Monday, q: It is raining, r: It is hot.

$$\neg q\rightarrow (r\wedge p)$$

Write each of the two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words of explanation. If you paid full price, you didn’t buy it at Crown Books. You didn’t buy it at Crown Books or you paid full price.