Assignment 12

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course MTH151

03/01/2014 at 10:40

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

012. The common sense of logic.

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Question: `q001. Note that there are 5 questions in this assignment.

Suppose I tell you 'If it rains today, I'll give you $100.' Under which of the following circumstances can you claim that I was not telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

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Your solution:

""2. It rains and I don't give you $100."" because the original statements says 'If it rains today, I'll give you $100.' So, if you don't give the $100, then you are not being truthful.

confidence rating #$&*: 3.

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Given Solution:

I said what would happen under a certain condition. In situation #2, that condition is fulfilled and what I said would happen doesn't happen. Therefore in situation #2 it is clear that I wasn't telling the truth.

In situation #3, the condition that I addressed isn't fulfilled so no matter what happens I can't be accused of not telling the truth. I said what would happen if rains. No matter what happens, if it doesn't rain what I said cannot be held against me.

It should be clear to anybody that situation #1 is exactly what you would expect, and that situation #4 is just would you would probably expect from my statement in the event that it doesn't rain, so nobody would say that this situation violates my claim to truthfulness.

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Self-critique (if necessary):

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Self-critique Rating:

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Question: `q002. Suppose that tell you 'It will rain today and I will give you $100'. Under which of the following circumstances can you claim that I was not telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. It doesn't rain and I don't give you $100.

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Your solution:

2. It rains and I don't give you $100 (because you don't give $100), 3. It doesn't rain and I give you $100 (because it doesn't rain), 4. It doesn't rain and I don't give you $100 (neither rains or gives $100) : all of these statements are false because either a part or the whole is not truthful.

confidence rating #$&*: 3.

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Given Solution:

It should be clear that situation #1 completely fulfills the conditions of my statement. Both of the things that I say will happen do happen.

In situation #2, it rains but you don't get the $100. I said two things were going to happen and one of them didn't. In that case you would have to say that I wasn't telling truth.

In situation #3, again one of the things I say is going to happen does but the other doesn't, so again you would have to say that I wasn't telling truth.

In situation #4, neither of the things I say will happen does and certainly it would have to be said that I wasn't telling truth.

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Self-critique (if necessary):

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Self-critique Rating:

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Question: `q003. Suppose that tell you 'It will rain today or I will give you $100, but not both'. Under which of the following circumstances can you claim that I was not telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

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Your solution:

Since ""or"" and ""but not both"" is incorporated, all are untruthful.

confidence rating #$&*: 2...

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Given Solution:

In situations 2 and 3, one of the things happens and the other doesn't, so you would not be able to say that I wasn't telling the truth. However in situation 1, both things happen, which I said wouldn't be the case; and in situation 4 neither thing happens. In both of these situations you would have to say that I was not telling truth.

STUDENT COMMENT:

:im not sure if I don’t understand or if there is just a typo present it would seem to me that 2 and 3 show that one situation was fulfilled and not the other which is what you said would happen

INSTRUCTOR RESPONSE:

In situation 1, I both things happen. However my statement include the phrase 'but not both'.

In situation 4, neither thing happens. My statement said that one would happen.

So in both situations 1 and 4, my statement fails to be true.

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Self-critique (if necessary):

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Self-critique Rating: 3.

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Question: `q004. Suppose that tell you 'It will rain today or I will give you $100'. Under which of the following circumstances can you claim that I was not telling the truth?

1. It rains and I give you $100.

2. It rains and I don't give you $100.

3. It doesn't rain and I give you $100.

4. I doesn't rain and I don't give you $100.

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Your solution:

Statement 3 (it doesn't rain and I give you $100): this would be true because of ""or"" in the original. Also, statement 2 would be true for the same reason. Statement 4 wouldn't necessarily be true or false. Statement 1 would be untruthful because both happens, which would nulify ""or"".

confidence rating #$&*: 2.

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Given Solution:

At first this might seem to be the same as the preceding problem. But in the preceding problem we specifically said '... but not both.' In this case that qualification was not made. Therefore we have regard the statement as true as long as at least one of the conditions is fulfilled. This is certainly the case for situation 1: both conditions are true we can certainly say that at least one is true. So in situation #1 we have to regard the present statement as true. So situation #1 would not be included among those in which I could be accused of not telling the truth.

STUDENT COMMENT:

Im not sure weather 2 was included in the statement that were not true

INSTRUCTOR RESPONSE:

In situation 2 one of the conditions was fulfilled, satisfying the original 'or' statement. So situation 2 doesn't contradict the original statement.

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Self-critique (if necessary):

This one was confusing. I kept thinking of the statements that were truthful. I think I understand, but could you explain the best way to think of this.

@&

If I say 'rain or $100' then as long as at least one of the two things occurs, rain or $100, you cannot say that I wasn't telling the truth.

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@&

Both doesn't nullify 'or'.

'or' is to be distinguished from 'exlusive or', in which case both would nullify it.

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Self-critique Rating: 2.

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Question: `q005. Suppose I make the statement 'The stock market will rise today or I will buy your dinner'. If the stock market does not rise today, is there something I can do or fail to do that would enable you to logically conclude that I wasn't telling the truth? If it is possible, specify what it is that I must do or fail to do. If it is not possible, explain why.

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Your solution:

""If the stock market doesn not rise today, and you don't buy dinner."" This statement would be untruthful because in the original it concludes that it will OR I will buy you dinner.

@&

At least one of the two conditions is true, either or both of which are sufficient to make the 'or' statement true, then the 'or' statement is true.

So there is nothing, once one of the statements becomes true, that can make the 'or' statement false.

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confidence rating #$&*:

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Self-critique Rating: Still a little mind boggled."

Self-critique (if necessary):

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Self-critique (if necessary):

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Self-critique rating:

#*&!

&#This looks good. See my notes. Let me know if you have any questions. &#