course Mth 151 r???D???z??m??assignment #014
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14:02:10 `q001. There are 8 questions in this set. If each of the propositions p and q can be either true or false, what combinations of truth values are possible for the two propositions (e.g., one possibility is that p is false and q is true; list the other possibilities)?
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RESPONSE --> p true q true p ture q false p false q false confidence assessment: 2
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14:02:44 It is possible that p is true and q is true. Another possibility is that p is true and q is false. A third possibility is that p is false and q is true. A fourth possibility is that p is false and q is false. These possibilities can be listed as TT, TF, FT and FF, where it is understood that the first truth value is for p and the second for q.
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RESPONSE --> I used the truth tables you show on the DVD. self critique assessment: 2
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14:05:10 p ^ q means 'p and q', which is only true if both p and q are true. In the case TT, p is true and q is true so p ^ q is true. In the case TF, p is true and q is false so p ^ q is false. In the case FT, p is false and q is true so p ^ q is false. In the case FF, p is false and q is false so p ^ q is false.
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RESPONSE --> I hit some in doing my answer so I just put it in here. Then looked at your explanation. p true q false p true q true p false q true p false q false self critique assessment: 3
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14:07:43 `q003. Write the results of the preceding problem in the form of a truth table.
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RESPONSE --> p true q true p ^ q true p ture q false p ^ q false p false q true p ^ q false p false q false p ^ q false confidence assessment: 2
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14:08:07 The truth table must have headings for p, q and p ^ q. It must include a line for each of the possible combinations of truth values for p and q. The table is as follows: p q p ^ q T T T T F F F T F F F F.
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RESPONSE --> I wasn't sure that that was what you were asking but I see that it was. self critique assessment: 2
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14:31:11 `q004. For each of the possible combinations TT, TF, FT, FF, what is the truth value of the proposition p ^ ~q?
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RESPONSE --> F, F, T, F. I went by the combined statement table confidence assessment: 1
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14:32:10 For TT we have p true, q true so ~q is false and p ^ ~q is false. For TF we have p true, q false so ~q is true and p ^ ~q is true. For FT we have p false, q true so ~q is false and p ^ ~q is false. For FF we have p false, q false so ~q is true and p ^ ~q is false.
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RESPONSE --> self critique assessment: 1
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14:48:37 `q005. Give the results of the preceding question in the form of a truth table.
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RESPONSE --> T, F, F, F confidence assessment: 2
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14:49:25 The truth table will have to have headings for p, q, ~q and p ^ ~q. We therefore have the following: p q ~q p^~q T T F F T F T T F T F F F F T F
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RESPONSE --> I used the wrong table. self critique assessment: 1
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15:09:22 `q006. Give the truth table for the proposition p U q, where U stands for disjunction.
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RESPONSE --> TT, T TF, T FT, T FF, F confidence assessment: 2
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15:10:05 p U q means 'p or q' and is true whenever at least one of the statements p, q is true. Therefore p U q is true in the cases TT, TF, FT, all of which have at least one 'true', and false in the case FF. The truth table therefore reads p q p U q T T T T F T F T T F F F
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RESPONSE --> Since one of them in all the groups except the last group they are all true. self critique assessment: 2
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15:11:45 `q007. Reason out the truth values of the proposition ~(pU~q).
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RESPONSE --> would all be false because p and q would be in the groups confidence assessment: 1
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15:12:58 In the case TT p is true and q is true, so ~q is false. Thus p U ~q is true, since p is true. So ~(p U ~q) is false. In the case TF p is true and q is false, so ~q is true. Thus p U ~q is true, since p is true (as is q). So ~(p U ~q) is false. In the case FT p is false and q is true, so ~q is false. Thus p U ~q is false, since neither p nor ~q is true. So ~(p U ~q) is true. In the case FF p is false and q is false, so ~q is true. Thus p U ~q is true, since ~q is true. So ~(p U ~q) is false.
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RESPONSE --> I forgot about the one that didn't contant either. self critique assessment: 2
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15:17:29 `q008. Construct a truth table for the proposition of the preceding question.
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RESPONSE --> T T F T confidence assessment: 1
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15:17:54 We need headings for p, q, ~q, p U ~q and ~(p U ~q). Our truth table therefore read as follows: p q ~q pU~q ~(pU~q) T T F T F T F T T F F T F F T F F T T F
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RESPONSE --> I wasn't sure if I did it right or not. self critique assessment: 1
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