Light of wavelength $\lambda$ is incident on a slit of width $d$. Under what conditions is the ray approximation valid? Under what circumstances does the slit produce enough diffraction to make the ray approximation invalid?

If Dr. Hardy is a department chairman, then he lives in Atlanta. He lives in Atlanta and his first name is Larry. Therefore. if his first name is not Larry, then he is not a department chairman. Is this argument valid or invalid?

Determine whether each argument is valid or invalid. All priests are Catholic.

$$\frac { \text {Some Catholics attend church every Sunday.} } { \therefore \text { Some priests attend church every Sunday.} }$$

Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. Given: If a figure is a square, it has four right angles. Figure A BCD has four right angles.

Use Euler diagrams to determine whether each argument is valid or invalid.

$$\begin{align*} &\text{All actors are artists.}\\ &\underline{\text{Tom Hanks is an artist.\ \ \ \ \ \ \ \ \ \ \ \ }}\\ &\text{Therefore, Tom Hanks is an actor.} \end{align*}$$

Use a truth table to determine whether the symbolic form of the argument is valid or invalid.

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

Translate each argument into symbo lic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. If I purchase season tickets to the footba ll games, then I do not attend all classes .

$$\frac { \text { If I do well in school. then I attend all classes .} } { \therefore \text { If I do not do well in schoo l, then I purchased season tickets to the football games.} }$$

State whether the following variable names are valid. If they are invalid, state the reason.

prod_a    c1234   abcd      _c3      12345
newamp    watts   $total    new$al  a1b2c3d4
9ab6      sum.of  average   volts1   finvolt

Write an if-else statement that determines whether the points variable is outside the range of 9 to 51. If the variable’s value is outside this range it should display “Invalid points.” Otherwise, it should display “Valid points.”

In this exercise, each argument has a true conclusion. Identify the argument as valid or invalid.

Amarillo is northeast of El Paso.

$$\underline{\textnormal{Amarillo is northeast of Deming.}\qquad\quad}$$

El Paso is northeast of Deming.

Determine whether the following symbolized arguments are valid or invalid by constructing a truth table for each.

$$\begin{aligned} &A \supset B\\ &(A \bullet B) \supset C\\ &\frac{A \supset(C \supset D)}{A \supset D} \end{aligned}$$

Use Euler diagrams to determine whether each argument is valid or invalid. All thefts are immoral acts.

$$\frac { \text {Some thefts are justifiable.} } { \text {Therefore , some immoral acts are justifiable .} }$$

In these exercises, each argument has a true conclusion. Identify each argument as valid or invalid.

Seattle is northwest of Boise.

Seattle is northwest of Salt Lake City.

Boise is northwest of Salt Lake City.

Use an Euler diagram to determine whether the syllogism is valid or invalid.
Some CD players are MP$3$ players.

$$\underline{\text{All iPods are MP3 players .}}$$

$\therefore$ Some CD players are iPods.