Exam 1: Thinking Critically

A set of propositions is listed. Draw a Venn diagram that represents all the information in the propositions and use it(and no other assumptions)to answer the question. Explain your reasoning. -All cars have wheels. All trucks have wheels. Some toys have wheels. No grandmothers have wheels. Question: Could a car be both a truck and a toy?

Two statements are listed in which p, q, and r represent propositions. Are the two statements logically equivalent? -not (p or q); (not p)and (not q)

Decide whether the statement makes sense. Explain your reasoning. -The time I spend studying is a subset of the time I spend playing basketball.

Write the negation of the proposition. -She earns more than me.

Make a truth table for the given statement. The letters p, q, r, s represent propositions. -if q, then not r

The argument contains an example of the fallacy named in parentheses. Explain how the fallacy occurs in the argument. -(Diversion)We've just remodeled the restaurant, so our food is delicious!

Choose the first set in the list natural numbers, whole numbers, integers, rational numbers, and real numbers thatdescribes the following number. -3406

Write the converse, inverse, or contrapositive off the proposition, as indicated. -If you received a refund of over $1000, then you cannot make a claim. (inverse)

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or notthe argument is valid. -Denying the conclusion

Analyze the situation and explain how you would make a decision. -You are flying out on Monday morning and returning home Tuesday night. You need to decide how to get to and from your home airport. Driving each way costs $2 in gas, and long-term parking costs $10 per full or partial day. If you take taxis, it will cost $11 each way. Which option is better?

A seemingly simple argument is given. Identify at least two hidden assumptions. -I should not go outside, because it is raining.

Use braces to write the members of the set, or state that the set has no members. -The days of the week

Analyze the situation and explain how you would make a decision. -The costs per day of driving to work are $5 for gas, $10 for parking, and $1 for wear-and-tear on the car. Taking the train to work costs $6.50 each way, plus $1.50 per day to park at the train station. Should you drive or take the train?

Decide whether the statement makes sense. Explain your reasoning. -I did not convince my friend that I was right, so I must not have argued logically.

Make a truth table for the given statement. The letters p, q, r, s represent propositions. -q and (not r)and s

Decide whether the statement makes sense. Explain your reasoning. -I drew a Venn diagram for two sets, and I only used one circle.

Create a simple three-line argument for the given form. Choose your example so that it illustrates clearly whether or notthe argument is valid. -Denying the hypothesis

Write the negation of the proposition. -Everyone is asleep.

Rephrase the statement as a conditional proposition with the form "if p, then q." -Cats chase mice.

Write the converse, inverse, or contrapositive off the proposition, as indicated. -If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive)