course There were a lot of things in these two sections that I was not able to really understand. I took one of the tests on Thursday afternoon, and I have a hard time with them. Usually on the work here, I can look at an example and use it to get an idea of what I'm doing in setting up other problems, on the tests I do not have that opportunity (obviously)which makes it much more difficult, coupled with the fact that I never do well on tests. ?????w??????eB???assignment #017017. Evaluating Arguments
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16:21:24 `q001. There are 9 questions in this set. Explain why [ (p -> q) ^ (q -> r) ^ p] -> r must be true for every set of truth values for which r is true.
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RESPONSE --> P Q R P->Q Q->R P->R _______ ______ ______ ______ T T T T T T T T F T F F T F F F T T F T T F T T F T F T T T F F T T T T F F F F F F confidence assessment: 1
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16:22:50 [ (p -> q) ^ (q -> r) ^ p] -> r must be true if r is true, since the statement can only be false if [ (p -> q) ^ (q -> r) ^ p] is true while r is false. Therefore the truth values TTT, TFT, FTT, FFT (i.e., all the truth values that have r true) all make the statement true.
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RESPONSE --> I think this is pretty much what I was trying to do, but it seems like I went a long route, and I'm not entirely sure I understand the whole thing. self critique assessment: 1
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16:24:38 `q002. At this point we know that the truth values TTT, TFT, FTT, FFT all make the argument [ (p -> q) ^ (q -> r) ^ p] -> r true. What about the truth values TTF?
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RESPONSE --> I think this would make the statement false because of the last value in the sequence being false = this makes the whole statement false. confidence assessment: 1
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16:26:10 It would be possible to evaluate every one of the statements p -> q, q -> r, etc. for their truth values, given truth values TTF. However we can shortcut the process. We see that [ (p -> q) ^ (q -> r) ^ p] is a compound statement with conjunction ^. This means that [ (p -> q) ^ (q -> r) ^ p] will be false if any one of the three compound statements p -> q, q -> r, p is false. For TTF we see that one of these statements is false, so that [ (p -> q) ^ (q -> r) ^ p] is false. This therefore makes the statement [ (p -> q) ^ (q -> r) ^ p] -> r true.
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RESPONSE --> I dont understand how the whole statement is true if one of the statements is false. It even states this in the answer provided here. It states that one of the statements if false, but overall it's true? self critique assessment: 1
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16:29:18 `q003. The preceding statement said that for the TTF case [ (p -> q) ^ (q -> r) ^ p] was false but did not provide an explanation of this statement. Which of the statements is false for the truth values TTF, and what does this tell us about the truth of the statement [ (p -> q) ^ (q -> r) ^ p] -> r?
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RESPONSE --> I have no idea how to set up this problem confidence assessment: 0
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16:30:34 p and q are both true, so p -> q and p are true. The only candidate for a false statement among the three statements is q -> r. So we evaluate q -> r for truth values TTF. Since q is T and r is F, we see that q -> r must be F. This makes [ (p -> q) ^ (q -> r) ^ p] false. Therefore [ (p -> q) ^ (q -> r) ^ p] -> r must be true, since it can only be false and if [ (p -> q) ^ (q -> r) ^ p] is true.
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RESPONSE --> Being able to see the way it is set up is helpful when seeing the answer. I have a lot of trouble trying to figure out the proper way to set up a problem in order to begin figuring out the answer. This causes me a lot of problem on the actual tests as well. self critique assessment: 2
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16:37:13 `q004. Examine the truth of the statement [ (p -> q) ^ (q -> r) ^ p] for each of the truth sets TFF, FTF and FFF.
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RESPONSE --> P Q R P->Q Q R ________ _____ ____ T F F T F F F F T F F T T F F F F F F F F [ (p -> q) ^ (q -> r) ^ p] [ (T-> F) ^ (T-> F) ^ F ] F F F confidence assessment: 1
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16:37:34 In the case TFF, p is true and q is false so p -> q is false, which makes [ (p -> q) ^ (q -> r) ^ p] false. In the case FTF, p is false, making [ (p -> q) ^ (q -> r) ^ p] false. In the case FFF, p is again false, making [ (p -> q) ^ (q -> r) ^ p] false.
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RESPONSE --> I think this is understood in my answer. self critique assessment: 2
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16:41:17 `q005. We have seen that for TFF, FTF and FFF the statement [ (p -> q) ^ (q -> r) ^ p] is false. How does this help us establish that [ (p -> q) ^ (q -> r) ^ p] -> r is always true?
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RESPONSE --> [ (p -> q) ^ (q -> r) ^ p] -> r [ (T-> T) ^ ( T->T) ^ T] -> T T T T Following the same formula and process as in the problem before, we got that the values were as shown above. Continuing on in that order (true to true, false to false) we got that each of them were true statements. confidence assessment: 2
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16:41:32 The three given truth values, plus the TTF we examined earlier, are all the possibilities where r is false. We see that in the cases where r is false, [ (p -> q) ^ (q -> r) ^ p] is always false. This makes [ (p -> q) ^ (q -> r) ^ p] -> r true any time r is false.
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RESPONSE --> self critique assessment: 0
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16:43:37 `q006. Explain how we have shown in the past few exercises that [ (p -> q) ^ (q -> r) ^ p] -> r must always be true.
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RESPONSE --> [ (p -> q) ^ (q -> r) ^ p] -> r in the past exercises, we found that each of the above statements were true through the process of the truth table. The three truths (pq, qr, p) all help to make the r true as well confidence assessment: 1
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16:45:15 We just finished showing that if r is false, [ (p -> q) ^ (q -> r) ^ p] is false so [ (p -> q) ^ (q -> r) ^ p] -> r is true. As seen earlier the statement must also be true whenever r is true. So it's always true.
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RESPONSE --> when I did the truth table, somehow I messed up on one of them, and confused two of the statements, which kept messing me up on the problem self critique assessment: 2
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16:47:55 `q007. Explain how this shows that the original argument about rain, wet grass and smelling wet grass, must be valid.
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RESPONSE --> if it rains (p) the grass is wet (q) we smell wet grass (r) it must have rained (p) It rained (p) the grass is wet (r) p->q r->p p->r confidence assessment: 2
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16:48:18 That argument is symbolized by the statement [ (p -> q) ^ (q -> r) ^ p] -> r. The statement is always true. There is never a case where the statement is false. Therefore the argument is valid.
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RESPONSE --> understood self critique assessment: 3
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16:50:43 `q008. Explain how the conclusion of the last example, that [ (p -> q) ^ (q -> r) ^ p] -> r is always a true statement, shows that the following argument is valid: 'If it snows, the roads are slippery. If the roads are slippery they'll be safer to drive on. It just snowed. Therefore the roads are safer to drive on.' Hint: First symbolize the present argument.
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RESPONSE --> it snows (p) the roads are slippery (q) If the roads are slippery (q) they'll be safer to drive on (r). It just snowed (p), therefore the roads are safer to drive on (r) confidence assessment: 2
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16:52:34 This argument can be symbolized by letting p stand for 'it snows', q for 'the roads are slippery', r for 'the roads are safer to drive on'. Then 'If it snows, the roads are slippery' is symbolized by p -> q. 'If the roads are slippery they'll be safer to drive on' is symbolized by q -> r. 'It just snowed' is symbolized by p. 'The roads are safer to drive on' is symbolized by r. The argument the says that IF [ p -> q, AND q -> r, AND p ] are all true, THEN r is true. In symbolic form this is [ (p -> q) ^ (q -> r) ^ p] -> r. This is the same statement as before, which we have shown to be always true. Therefore the argument is valid.
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RESPONSE --> This is somewhat understood, though in my answers I am not totally following the set up of each one. That is where I am having the most difficulty. Sometimes I can uderstand how things go in the order but I cannot set it up properly self critique assessment: 2
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16:54:45 `q009. Symbolize the following argument and show that it is valid: 'If it doesn't rain there is a picnic. There is no picnic. Therefore it rained.'
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RESPONSE --> if it doesnt rain (p) there is a picnic (q). There is no picnic q) therefore it rained (p). [(p->q) ^ (q->p) T T T confidence assessment: 1
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16:55:37 We could let p stand for 'it rained', q for 'there is a picnic'. The first statement is 'If it doesn't rain there is a picnic', which is symbolized by ~p -> q. The second statement, 'There is no picnic', is symbolized by ~q. The conclusion, 'it rained', is symbolized by p. The argument therefore says IF [ (~p -> q) AND ~q ], THEN p. This is symbolized by [ (~p -> q) ^ ~q ] -> p. We set up a truth table for this argument: p q ~p ~q ~p -> q (~p -> q) ^ ~q [ (~p -> q) ^ ~q ] -> p T T F F T F T T F F T T T T F T T F T F T F F T T F F T
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RESPONSE --> I think I am having the most problems with knowing how to set up each problem, when to use what functions, and when to use the truth table to come to the correct conclusions. self critique assessment: 2
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b???????i???????assignment #018 018. Base-10 Place-value Number System Liberal Arts Mathematics I 07-15-2007
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17:01:46 `q001. There are 5 questions in this set. From lectures and textbook you will learn about some of the counting systems used by past cultures. Various systems enabled people to count objects and to do basic arithmetic, but the base-10 place value system almost universally used today has significant advantages over all these systems. The key to the base-10 place value system is that each digit in a number tells us how many times a corresponding power of 10 is to be counted. For example the number 347 tells us that we have seven 1's, 4 ten's and 3 one-hundred's, so 347 means 3 * 100 + 4 * 10 + 7 * 1. Since 10^2 = 100, 10^1 = 10 and 10^0 = 1, this is also written as 3 * 10^2 + 4 * 10^1 + 7 * 10^0. How would we write 836 in terms of powers of 10?
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RESPONSE --> six 1's, three 10's, and eight 100's 8 * 100 + 3*10 + 6*1 8*10^2 + 3*10^1 + 6*10^0 confidence assessment: 3
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17:01:57 836 means 8 * 100 + 3 * 10 + 6 * 1, or 8 * 10^2 + 3 * 10^1 + 6 * 10^0.
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RESPONSE --> understood self critique assessment: 3
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17:04:02 `q002. How would we write 34,907 in terms of powers of 10?
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RESPONSE --> 30*10^4 + 9*10^2+0*10^1+7*10^0 confidence assessment: 2
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17:05:27 34,907 means 3 * 10,000 + 4 * 1000 + 9 * 100 + 0 * 10 + 7 * 1, or 3 * 10^4 + 4 * 10^3 + 9 * 10^2 + 0 * 10 + 7 * 1.
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RESPONSE --> The last part of the answer (3 * 10^4 + 4 * 10^3 + 9 * 10^2 + 0 * 10 + 7 * 1.) is what I was trying to get to, but I think I got a couple of things out of order, but all-in-all, I pretty much understand the concept self critique assessment: 2
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17:06:01 `q003. How would we write .00326 in terms of powers of 10?
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RESPONSE --> I am not sure how to do the problem in a dec. form. confidence assessment: 0
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17:07:22 First we note that .1 = 1/10 = 1/10^1 = 10^-1, .01 = 1/100 = 1/10^2 = 10^-2, .001 = 1/1000 = 1/10^3 = 10^-3, etc.. Thus .00326 means 0 * .1 + 0 * .01 + 3 * .001 + 2 * .0001 + 6 * .00001 = 0 * 10^-1 + 0 * 10^-2 + 3 * 10^-3 + 2 * 10^-4 + 6 * 10^-5 .
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RESPONSE --> I mostly understand this problem after seeing it worked, but I am not the worlds greatest math mind and I'm not sure I understand this enough to work it without being able to look at one that has already been worked. self critique assessment: 2
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17:09:08 `q004. How would we add 3 * 10^2 + 5 * 10^1 + 7 * 10^0 to 5 * 10^2 + 4 * 10^1 + 2 * 10^0?
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RESPONSE --> 30,507+50,420 confidence assessment: 1
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17:10:34 We would write the sum as (3 * 10^2 + 5 * 10^1 + 7 * 10^0) + (5 * 10^2 + 4 * 10^1 + 2 * 10^0) , which we would then rearrange as (3 * 10^2 + 5 * 10^2) + ( 5 * 10^1 + 4 * 10^1) + ( 7 * 10^0 + 2 * 10^0), which gives us 8 * 10^2 + 9 * 10^1 + 9 * 10^0. This result would then be written as 899.
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RESPONSE --> I totally messed this problem up in my answer! I have looked at this problem for awhile and cannot figure out how they came to the answer of 899. Could you provide a bit more explination? self critique assessment: 1
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17:11:34 `q005. How would we add 4 * 10^2 + 7 * 10^1 + 8 * 10^0 to 5 * 10^2 + 6 * 10^1 + 4 * 10^0?
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RESPONSE --> 912? (I'm sure I have this wrong) confidence assessment: 0
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17:12:49 We would write the sum as (4 * 10^2 + 7 * 10^1 + 8 * 10^0) + (5 * 10^2 + 6 * 10^1 + 4 * 10^0) , which we would then rearrange as (4 * 10^2 + 5 * 10^2) + ( 7 * 10^1 + 6 * 10^1) + ( 8 * 10^0 + 4 * 10^0), which gives us 9 * 10^2 + 13 * 10^1 + 12 * 10^0. Since 12 * 10^0 = (2 + 10 ) * 10^0 = 2 * 10^0 + 10^1, we have 9 * 10^2 + 13 * 10^1 + 1 * 10^1 + 2 * 10^0 = 9 * 10^2 + 14 * 10^1 + 2 * 10^0. Since 14 * 10^1 = 10 * 10^1 + 4 * 10^1 = 10^2 + 4 * 10^1, we have 9 * 10^2 + 1 * 10^2 + 4 * 10^1 + 2 * 10^0 = 10^10^2 + 4 * 10^1 + 2 * 10^0. Since 10*10^2 = 10^3, we rewrite this as 1 * 10^3 + 0 * 10^2 + 4 * 10^1 + 2 * 10^0. This number would be expressed as 1042.
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RESPONSE --> I am simply not able to understand this one. I can do pretty good for the most part in working it backwards from the answer, but I cant really process it backwards from the problem to get the answer. self critique assessment: 1
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