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Writing Simple Arguments in Standard Form

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What are the standard forms of the arguments that follow?

a. Women live longer than men, on the average. So, you will probably live longer than your husband!

b. Subliminal advertising is quite common. Why? Hundreds of studies have
shown that subliminal persuasion works. You end up buying things you neither want nor need: like a singing, flipping fish on a board!

c. You should believe in God. If God doesn't exist, then all you've lost is a few Sunday mornings at church. But if God does exist, then you have gained eternal

d. It would be foolish to permit the sale of marijuana to seriously ill people on the recommendation of their physicians. That just opens the floodgates to the complete legalization of that dangerous drug.

e. "Women have rights," said the Bullfight Association president, "But women
shouldn't fight bulls because a bullfighter is and should be a man."

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Solution Preview

In a sense, each of the questions is asking you for the same thing: tell the professor the standard form of the argument. Although different professors may mean different things by 'standard form', there is a good chance that your professor wants you to re-write each of the arguments in what is known as standard categorical form. Standard categorical form is simply a way of making sure arguments following a definite, known pattern, so that confusion and ambiguity can be reduced. Here is an example of an argument in ordinary English, and then of the same argument in standard categorical form:

"That was the stupidest movie I've ever seen. There's no way it will last two weeks!"

What the person making this claim is trying to argue is pretty simple: the money he just saw is so bad that it won't possibly last two weeks. The first step in writing an argument is standard categorical form is to identify the conclusion -- what is the person trying to prove? HEre, the conclusion is:

Conclusion: There is no way this movie will last two weeks.

Okay, so we know what the conclusion is. But what about the premise(s). Well, one of them is clearly ...

Solution Summary

The solution gives an in-depth explanation of how to turn regular everyday arguments into their standard form versions, complete with an example, so that the reader can do the same to the ones in the question. 792 words.

Similar Posting

Statements, Logical Connectives and Truth tables.

Here are some questions from a study packet for my final. I would like solutions and explanations so that I may practice before my big test. Thanks!

1. Write a simple sentence and then write the negation. Imagine situations where each statement is true or false. How does the truth value (true or false) of the negation statement compare with the truth value of the original statement?

2. Write two simple sentences and then write the compound statement you get from connecting the original two statements using the word "and." Imagine situations where each simple statement is true or false. How does the truth value (true or false) of the compound statement compare with the truth value of the original statements?

Here are symbols you may need:      U ∩  [ ] COPY AND PASTE!

3. Let p, q, and r be the following statements:
p: It is raining.
q: The clouds are dark.
r: The temperature is dropping.

Translate the following statements into English
(a) p  r (b) ~p  (q  r) (c) q  r (d) (  r   q)   p

4. Write in symbolic form using p, q, r, , , , , where p, q, r represent the following statements:

p: A dog is friendly.
q: A dog has a long tail.
r: A dog licks faces.

(a) If a dog has a long tail, then it is not friendly.
(b) If a dog is not friendly, then it does not lick faces.
(c) If a dog has a long tail, then either the dog is friendly or the dog licks faces.
(d) If a dog licks faces, then the dog is friendly and the dog has a long tail.

5. Fill the headings of the following truth table using p, q, , , , and .

p q (b)
p q (a)
(a) (b)

6. For each of the following conditionals, identify the antecedent and the consequent. Form the converse, inverse, and contrapositive.

(a) If I go to work, then I will get paid.
(b) Your yard will not look good if you don't mow the grass.

7. Rewrite ~ (p  ~q) using DeMorgan's laws.

8. (a) Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.

If it is raining, then we will close the window.
We closed the window.
 It is raining.

9. Use an Euler diagram to determine whether the syllogism is valid or invalid

All doctors are helpful.
Some doctors are female.
 Some helpful people are female.

10. Construct a truth table for ~q  (q  p).

Here are symbols you may need:      U ∩  [ ] COPY AND PASTE!

11. Write the negation for the statement below.

Someone in the family makes bread.

12. Let p, q, and r be the following statements:

p: Mary is on the bus.
q: April is in the car.
r: Stan is at the zoo.

Translate the following statement into English: (p   r)  q

13. Write the following compound statement in symbolic form

Let p: Today is Friday.
q: Tomorrow is not the day to go shopping.
If tomorrow is not the day to go shopping, then today is not Friday.

14. Construct a truth table for  (p  q)

15. Write the converse, inverse, and contrapositive of the following conditional statement

If the sun is shining, then it will not rain.

16. Determine whether the argument is valid or invalid.

A tree has green leaves and the tree produces oxygen.
This tree has green leaves
 This tree produces oxygen.

17. Use Euler Diagrams to determine whether the following syllogism is valid or invalid.

All golfers have golf carts.
All members of the A club have golf carts.
 All members of the A club are golfers

18. Determine the truth value of the statement q  [ r  (p  q)] when p is false, q is true, and r is true.

19. Determine the truth value of the following statement:

Rembrandt was a famous painter and all prime numbers are odd.

20. Use De Morgan's Laws to determine whether the two statements are equivalent

 (p  q),  p  q

21. Determine which, if any, of the three statements are equivalent.

a) If today is Monday, then tomorrow is Tuesday.
b) If today is not Monday, then tomorrow is not Tuesday.
c) If tomorrow is not Tuesday, then today is not Monday.

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