SOLUTION: Please Help. I'm so confused and lost with theese questions. 1. Write a negation of the statement. All squares are parallelograms. All squares are not parallel

Question 276673: Please Help. I'm so confused and lost with theese questions.
1. Write a negation of the statement.
All squares are parallelograms.

All squares are not parallelograms.
No squares are parallelograms.
Some squares are parallelograms.
Some squares are not parallelograms.

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

p: Jamie is on the train.
q: Sylvia is at the park.
r: Nigel is in the car.

Translate the following statement into English: (p q) r
3. Construct a truth table for ~q p
4. Construct a truth table for (p ~q) ↔ q
5. Let p represent the statement, "Jim plays football", and let q represent "Michael plays basketball". Convert the compound statements into symbols.
Jim does not play football or Michael does not play basketball.
(Points :3)
~(p q)
p q
~p ~q
~p ~q

6. Write the compound statement in words.
Let p = The monitor is included.
q = The color printer is optional.
p ~q

The monitor is not included and the color printer is optional.
The monitor is included and the color printer is not optional.
The monitor is included and the color printer is optional.
The monitor is included or the color printer is not optional.

7. Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
p (q ~r)
True
False

8. Determine which, if any, of the three statements are equivalent.
I) If it is dark outside, then I will not be on time for dinner.
II) If it is not dark outside, then I will be on time for dinner.
III) If I will be on time for dinner, then it is not dark outside.
I, II, and III are equivalent
I and III are equivalent
II and III are equivalent
I and II are equivalent
None are equivalent

9. Given the argument and its Euler diagram below, determine whether the syllogism is valid or invalid.

Valid
Invalid

10. Identify which argument is invalid.

If Rita watches the movie, then she will not exercise.
Rita did not watch the movie.
Therefore, Rita exercised.

If Sandra pays her all taxes on time, then she will not incur a penalty.
Sandra incurs a penalty.
Therefore, she did not pay her taxes on time.

Either Sandra pays her all taxes on time or she will incur a penalty.
Sandra did not pay all her taxes in time.
Therefore, she will incur a penalty.

If Jan gets lost, she will need a map.
Jan does not need a map.
Therefore, Jan is not lost.

If Juanita hits all the high notes, she will not be embarrassed.
Juanita hit all the high notes.
Therefore, she was not embarrassed.

11.
Write the statement in symbols using the p and q given below. Then construct a truth table for the symbolic statement and select the best match.
p = The forest is dark.
q = The moon is full.
The forest is dark or the moon is full.
p q
p q p q
T T F
T F T
F T T
F F F
p q
p q p q
T T T
T F T
F T T
F F F
p q
p q p q
T T T
T F F
F T F
F F T
p q
p q p q
T T T
T F F
F T F
F F F

12. Determine if the argument is valid or invalid. Give a reason to justify answer.
If you eat well, you will be well.
If you are well, you will be happy.
If you eat well, you will be happy.
Valid by the law of detachment
Valid by the law of contraposition
Invalid by fallacy of the converse
Invalid by fallacy of the inverse
Valid by the law of syllogism
Valid by disjunctive syllogism

Answer by amyd62(1) (Show Source): You can put this solution on YOUR website!

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