91Ó°ÊÓ

Use modus ponens or modus tollens to fill in the blanks in the arguments of 1-5 so as to produce valid inferences. If \(\sqrt{2}\) is rational, then \(\sqrt{2}=a / b\) for some integers \(a\) and \(b\). It is not true that \(\sqrt{2}=a / b\) for some integers \(a\) and \(b\). ______________

Use modus ponens or modus tollens to fill in the blanks in the arguments of 1-5 so as to produce valid inferences. If this is a while loop, then the body of the loop may never be executed. ______________ The body of the loop may never be executed.

Rewrite the statements in \(1-4\) in if-then form. I am on time for work if I catch the \(8: 05\) bus.

Represent the decimal integers in 1-6 in binary notation. 55

Use modus ponens or modus tollens to fill in the blanks in the arguments of 1-5 so as to produce valid inferences. If logic is easy, then I am a monkey's uncle. I am not a monkey's uncle. ______________

Rewrite the statements in \(1-4\) in if-then form. Fix my ceiling or I won't pay my rent.

Indicate which of the following sentences are statements. a. 1,024 is the smallest four-digit number that is a perfect square. b. She is a mathematics major. c. \(128=2^{6}\) d. \(x=2^{6}\)

Represent the decimal integers in 1-6 in binary notation. 1609

Write the statements in 6-9 in symbolic form using the symbols \(\sim, \vee\), and \(\wedge\) and the indicated letters to represent component statements. Let \(s=\) "stocks are increasing" and \(i=\) "interest rates are steady." a. Stocks are increasing but interest rates are steady. b. Neither are stocks increasing nor are interest rates steady.

Use truth tables to determine whether the argument forms in 6-10 are valid. Indicate which columns represent the premises and which represent the conclusion, and include a few words of explanation to support your answers. $$ \begin{aligned} & p \\ & p \rightarrow q \\ & \sim q \vee r \\ \therefore & r \end{aligned} $$