Nimo M.

asked • 10/29/15

For each of the following arguments, explain whether correct reasoning is used.

1. Hanoch is rich because he doesn't pay taxes and he doesn't pay taxes because he is rich.
2. All mammals have a backbone and species A has a backbone, so it must be mammal.
3. All mammals are warm blooded and species A is a mammal so species A is warm blooded.
4. Peter said an election will be called this spring, but he is a liar so there will be no election.

1 Expert Answer

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Arnold F. answered • 10/29/15

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1. You're missing a conclusion here
 
2. (M→B )∧(A→B) ∴ (A→M)     not valid
 
3. (M→W)∧(A→M) ∴ (A→W)     valid, Hypothetical syllogism
 
4. (P→E )∧(¬P) ∴ (¬E)           not valid
 
If you have done truth tables then you can prove/disprove the validity of an argument by testing:
 
(Premise1 ∧ Premise2 ∧ ... ∧ Premisej ) → conclusion
 
 
Any questions comment back.
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Nimo M.

1.) The conclusion is he doesn't pay taxes because he is rich.
2.) How is 2 not valid. They used a premises
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10/29/15

Stefan F.

"2.) How is 2 not valid. They used a premises"
 
All mammals have a backbone.  --> That does NOT imply that non-mammals cannot have backbones.
 
(i.e. "All mammals have a backbone and some non-mammals could also have a backbone.")
 
Species A has a backbone.  This does not imply that species A is a mammal (see statement in parentheses).
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10/29/15

Nimo M.

So 2 is valid
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10/29/15

Arnold F.

For an argument to be valid it must be always true. That is when the premises are true then conclusion MUST always be true not true just sometimes.
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10/29/15

Arnold F.

That means A → M might be true but the premises must actually show it is always true which they do NOT show! Therefore it is not a valid argument.
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10/29/15

Arnold F.

In the first one by AND do you mean THEN because in logic the conclusion of an argument is not preceded by the word AND.
 
If so then it becomes  (R→N) → (N→R)  which is not valid.
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10/29/15

Nimo M.

But AND was used in #3 and it's valid
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10/29/15

Arnold F.

AND is allowed before a premise but not the conclusion. in #3 the word SO has the same meaning as THEN or THEREFORE and several other words that ARE allowed before the conclusion.
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10/29/15

Nimo M.

So Number 1 is invalid because there is no conclusion in the statement
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10/30/15

Arnold F.

The way the English is written that's right.
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10/30/15

Nimo M.

She writes the following 64/16 = 4/1=4. She crossed out the two 6s.
She asks her dad if 64/16=4 and her day says yes. Fadi believes she has mastered simplifying fractions.
1. Is Fadi's approach reasonable? Explain.
2. Suppose you try to correct Fadi. What could you tell her if she argues that her method produces the correct answer and therefore she must be correct.
 
no one is answering this question. Mr.F could you please answer it. Thank you
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10/30/15

Arnold F.

1. Reasonable, yes. She sees a four on top and a four on the bottom so she crossed them out.
 
2. Step(s) that produce the result you are looking for might not be the correct steps. You're outside a house and the door is locked but want to get inside so drive a car through the door and you end up inside the house. 
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10/30/15

Arnold F.

Nimo, Did you give any thought about using my tutoring services?
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10/30/15

Nimo M.

I'm still think about it. 
I posted these question but no one is answering them also. Could you please help me Mr.F
 
Four balances are shown where the two sides of each contain exactly the same amount of weight. Determine how many green circles are required in the fourth balance. Explain/ show how this was determined.

First balance has 4 squares, 1 triangle, 1 circle, and 2 diamonds.
Second balance has 1 triangle, 1 square, and 1 circle.
Third balance has 1 triangle, 1 diamond, 1 circle, and 2 squares.
Fourth balance ( how many green circles does it have?)
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10/30/15

Arnold F.

If each is a "balance" shouldn't you be given each side of the balance?
 
If the first and second are the two sides of a single balance then that can't happen.
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10/30/15

Nimo M.

I don't understand what do you mean it can't happen. They want to know how many green circles are in the fourth balance
1st balance has 4 squares, 1 triangle, 1 circle, and 2 diamonds.
2nd balance has 1 triangle, 1 square, and 1 circle.
3rd balance has 1 triangle, 1 diamond, 1 circle, and 2 squares.
4th balance has 1 triangle, 1 diamond, and 1 square but how many green circles does it have
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10/30/15

Arnold F.

In the first balance what is on the left and what is on the right?
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10/30/15

Nimo M.

For the 1st balance 4 squares, 1 triangle, and a circle are on the left. 2 diamonds are on the right.
For the 2nd balance 1 triangle, and 1 square are on the left and a circle on the right.
For the 3rd balance 1 triangle, and 1 diamond is on the left and 1 circle, 2 squares is on the right.
For the 4th balance 1 triangle, 1 diamond, and 1 square is on the left, but how many circles are on the right.
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10/30/15

Arnold F.

That gives four equations:
 
4S + T  + C =2D
  S + T         =C
        T + D = C + 2S
        T  + D +S = ?C
 
OR
 
4S + T + C -2D = 0
  S + T - C        =0
-2S + T - C + D =0
   S + T -?C +D =0
 
Use simultaneous equations or if you did it is class matrix diagonalization to solve.
 
See if you can finish from here.  
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10/30/15

Nimo M.

I don't know how to solve it?
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10/30/15

Arnold F.

Nimo, It's a lengthy explanation not well suited for this type of interaction. If you did this type of problem in class i would suggest that you check your notes. If you want a personalized lesson online I could give you a discount for the first tutoring hour. Let me know. Dr. F.
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10/30/15

Nimo M.

I never did this type of equation doesn't this have to do with logic and reasoning.
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10/30/15

Nimo M.

Would you help me with these questions.
1.) Brianna has a pet bunny named Sir Fluffles. Sir Fluffles is capable of hopping up either one step or two steps at a time. How many different ways could Sir Fluffles climb a flight of six stairs? Explain.
(Hint: Let S represent a single step and D represent a double step. SSSSD, SSDSS, and DDD are three different ways of hopping up the six stairs.)
 
2.) Tulia and Ian are debating Albertan culture.
Tulia: All Albertan like to eat beef.
Ian: I have a counterexample. Mike lives in Alberta and he is a vegetarian.
Tulia: He doesn't like beef, so he's not a true Albertan. As such, he cannot be a counterexample.
Whose reasoning is correct? Is Mike a counterexample? Explain.
 
3.) Describe why the following is a paradox.
The following sentence is true.
The previous sentence is false.
 
 
4.) Fernando wears three colors of socks: red, blue, and white. He doesn't pair his socks when he washes them, he just throws them into his sock drawer.

What is the fewest number of socks Fernando needs to take out of the drawer to guarantee he has a matching pair? Explain.
 
Is there a fewest number of socks he could take out to guarantee that he will have a red pair? Explain.

5.) Prove the following conjecture.
Between any two unique Real Numbers, there exists another Real Number.
 
The proof may be started with Let x and Y represent two different Real Numbers. 
 
6.) An undisclosed number of friends meet for dinner. Each person shakes each other person's hand exactly once. How many handshakes occur?
Piti reasons that 2 people will have one handshake. For each person added, everyone in the earlier group will need to shake the new person's hand. So, when a third person is added there will be two new handshakes and therefore 1+2=3 handshakes altogether. Similarly, when the fourth person is added there will be 1+2+3=6 handshakes and when the fifth person is added there will be 1+2+3+4=10 handshakes.
Piti concludes that if n people attend a party, there will be 1+2+3+ ....+(n-1) handshakes altogether.
Piti's argument includes both inductive and deductive reasoning.

Explain how Piti's argument is inductive.
 Explain how Piti's argument is deductive.
 
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10/30/15

Arnold F.

Nimo, These might be questions from your text or from your teacher but they can't just be answered briefly in the context of this "answers" web page. That's probably why no one answered them. I'm sorry i don't have any better option for you. Just answering these questions fully in a one on one setting could take the better part of an hour.
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10/30/15

Nimo M.

Mr.F could you please help me with questions 2,3,4, and 5.
Thank you
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11/03/15

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