Exam 3: Logic

Identify the statement as a conjunction, disjunction, conditional, or biconditional. If Jon fails this test, then he will fail the course.

Determine the validity of the following argument. \simq\rightarrowp q \therefore\simp

Determine whether the statement is a tautology, a self-contradiction, or neither. $( p \leftrightarrow q ) \wedge ( p \leftrightarrow q )$

Determine the validity of the following argument. \simp\rightarrowq q\rightarrow\simr \therefore\simp\rightarrow\simr

Let p = "Daphne speaks Spanish." Let q = "Daphne speaks French." Write the following statement in symbols. Daphne speaks Spanish if and only if Daphne speaks French.

Write the negation of the statement. Everyone at my house got the flu.

Write the converse of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. If Paolo does not bicycle to school, then Roberto does not drive to school.

Identify $p$ and $q$ . Then translate the argument into symbols and determine whether it is valid or invalid. I will order pizza or Chinese food. I did not order Chinese food. $\therefore$ I ordered pizza.

Complete the following truth table. p q p\veeq \sim(p\veeq) \sim(p\veeq)\rightarrowp

Determine whether the argument is valid or invalid. Some items are non-sale items. No non-sale item is affordable. $\therefore$ Some items are not affordable.

Write the negation of the statement. She is not angry.

Determine whether the argument is valid or invalid. All $B$ is $C$ . All $C$ is $A$ . $\therefore$ All $B$ is $A$ .

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies. \simp\rightarrowq \simq \thereforep

Write the argument in symbols; then decide whether the argument is valid by using the common forms of valid arguments and fallacies. You ate what was in your lunchbox or you didn't get an A. You didn't get an $\mathrm { A }$ $\therefore$ You didn't eat what was in your lunchbox A) Invalid p\rightarrowq \simq \therefore\simp B) Valid p\rightarrowq \simq \therefore\simp C) Valid p\rightarrowq \simq \therefore\simp D) Invalid p\rightarrowq \simq \therefore\simp

Let p = "My homework is finished." Write the following statement in symbols. It is not true that my homework is finished.

Identify $p$ and $q$ . Then translate the argument into symbols and determine whether it is valid or invalid. If I finish studying, then I will watch television. I did not finish studying. $\therefore$ I did not watch television.

$\text { Complete the following truth table for the statement } p \vee \sim q \text {. }$ p q p\vee\simq a) p q p\vee\simq B) p q p\vee\simq C) p q p\vee\simq D) p q p\vee\simq

Let p = "Ed plays the guitar." Let q = "Ed plays the piano." Write the following statement in symbols. Ed plays the guitar, and Ed does not play the piano.

$\text { Complete the following truth table. }$ p q p\leftrightarrowq A) p q p\leftrightarrowq B) p q p\leftrightarrowq C) p q p\leftrightarrowq D) p q p\leftrightarrowq