course Mth 151 zŜdžefLassignment #014
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16:48:21 `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 Q T T T F F T F F confidence assessment: 3
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16:48:27 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 --> OK self critique assessment:
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16:49:36 `q002. For each of the for possibilities TT, TF, FT and FF, what is the truth value of the compound statement p ^ q ?
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RESPONSE --> p q P and Q T T T T F F F T F F F F confidence assessment: 3
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16:49:43 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 --> OK self critique assessment: 3
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16:50:30 `q003. Write the results of the preceding problem in the form of a truth table.
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RESPONSE --> p q p^q T T T T F F F T F F F F confidence assessment: 3
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16:50:38 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 --> OK self critique assessment: 3
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16:51:31 `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 --> p q p or not q T T T T F T F T F F F T confidence assessment: 3
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16:52:01 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 --> OK self critique assessment: 3
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16:52:20 `q005. Give the results of the preceding question in the form of a truth table.
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RESPONSE --> p q ~q p^~q T T F F T F T T F T F F F F T F confidence assessment: 3
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16:52:26 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 --> OK self critique assessment: 3
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16:53:07 `q006. Give the truth table for the proposition p U q, where U stands for disjunction.
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RESPONSE --> Assuming that U means ""or"" p q p U q T T T T F T F T T F F F confidence assessment: 3
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16:53:15 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 --> OK self critique assessment: 3
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16:58:07 `q007. Reason out the truth values of the proposition ~(pU~q).
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RESPONSE --> TT p is true and q is true, so ~q is false. p or~q is true, since p is true. So ~(p U ~q) is false. TF p is true and q is false, so ~q is true. p U ~q is true, since p is true (as is q). So ~(p U ~q) is false. FT p is false and q is true, so ~q is false. p U ~q is false, since neither p nor ~q is true. So ~(p U ~q) is true. FF p is false and q is false, so ~q is true. p U ~q is true, since ~q is true. So ~(p U ~q) is false. confidence assessment: 3
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16:58:21 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 --> OK self critique assessment: 3
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16:59:17 `q008. Construct a truth table for the proposition of the preceding question.
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RESPONSE --> 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 confidence assessment: 2
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16:59:30 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 --> Awesome! OK self critique assessment: 3
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