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1. Construct a truth table for (p Λ q) → ~p. Be sure to include all intermediate steps in the table.

3. Construct a truth table for p ↔ (q V ~ p). Include all intermediate steps in the table.

4. Given p is true, q is true, and r is false, find the truth value of the statement ~q → (p V r).

5. Write the argument below in symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q used.

If the gazebo is made of wood, then the vine is growing on the gazebo.
The vine is growing on the gazebo.
Therefore the gazebo is made of wood.

6. Determine which, if any, of the following three statements are equivalent and why.

I) Gasoline costs $1.99 per gallon if and only if you live in Orange County.
II) You do not live in Orange County and gasoline does not cost $1.99 per gallon.
III) If you do not live in Orange County then gasoline does not cost $1.99 per gallon.

7. Create a Euler diagram to determine whether the syllogism is valid or invalid.
All children like games.
Eli is a child.
Therefore Eli likes games.

8. If the argument below is valid, name which of the four valid forms of argument is represented. If it is not valid, name the fallacy that is represented.

If Sally is on vacation, then Tom is at work.
If Tom is at work, then the line at the post office is long.
Therefore, if Sally is on vacation, then the line at the post office is long.

9. If p is true, q is false, and r is true, find the truth value of the statement.
r → (~p↔~q)

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Write the argument below in symbols to determine whether it is valid or invalid.

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Valid or Invalid Syllogisms

Hypothetical syllogisms (conditional arguments) can have two valid and two invalid structures. The two valid structures are affirming the antecedent (modus ponens) and denying the consequent (modus tollens). The two invalid structures, or fallacies, are denying the antecedent and affirming the consequent. Please help me determine if the arguments below are valid or invalid and what form they take and check the first one i did please. Thank you.

1. Chris and Nick would be very happy if the Browns beat the Steelers. The Browns did beat the Steelers, so Chris and Nick are very happy, indeed.

Valid Modus Ponens (Affirming the Antecedent)

2. Madeline must have known the material for the test, because if a person knows the material, that person will get an A, and Madeline was one of the students that got an A.

3. Anastasia believes that if she treats people honestly and with an open mind, she will have diverse friendships. She is honest and open-minded and has friends all over the world.

4. Roberto thought that if he worked very hard, his boss would give him a raise or a promotion. He made sure she noticed him, but she did not give him a raise or promotion. He thought he must not have worked hard enough.

5. "I'm still eating too much ice cream," lamented George. "My waist measurement is the same as it was six months ago. I know if I didn't eat so much ice cream, I would reduce my waist size."

6 The best way to make sure we pay fewer taxes is to elect conservatives. We must not have elected enough conservatives, because we are paying more taxes.

7 If my neighbor were a decent human being, he wouldn't let his yard trash fall onto my property. But he's not a decent human being, so we get to clean his trash as well as ours.

8 We'll have fun and learn a lot in this course, if we have great facilitator. We do have a great facilitator; therefore we are learning a lot and having fun doing it!

9 If I could understand the concept of hypothetical syllogisms, I would get a passing grade. Hurray! I got a passing grade, so I must have understood the concept of hypothetical syllogisms.

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