course MTH 151
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18:04:21 `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-T & q-F p-T & q-T p-F & q-T p-F & q-F confidence assessment: 1
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18:04:36 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 --> correct self critique assessment: 3
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18:08:11 `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 --> TT- p & q are both true TF-p is true q is false FT-p is false q is true FF-p is false q is false TT-p ^ q would be the true statment since they are both true confidence assessment: 1
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18:08:28 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 --> correct self critique assessment: 3
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18:10:38 `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: 2
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18:10:49 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 --> correct self critique assessment: 3
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18:15:58 `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 --> TT-p is true ~q is false FT-p is true ~q is true FT-p false ~q is false FF-p false ~q is true FT-would be the true statement confidence assessment: 1
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18:16:06 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 --> correct self critique assessment: 3
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18:18:39 `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: 1
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18:18:51 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 --> correct self critique assessment: 3
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18:20:37 `q006. Give the truth table for the proposition p U q, where U stands for disjunction.
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RESPONSE --> p q pVq T T T T F T F T T F F F confidence assessment: 1
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18:20:51 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 --> correct self critique assessment: 3
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18:27:09 `q007. Reason out the truth values of the proposition ~(pU~q).
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RESPONSE --> TT-p is true ~q is false TF-p is true ~q is true FT-p is false ~q is false FF-p is false ~q is true ~(pV ~q) would be true according to FT confidence assessment: 1
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18:27:22 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 --> correct self critique assessment: 3
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18:29:01 `q008. Construct a truth table for the proposition of the preceding question.
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RESPONSE --> p q ~q pV ~q ~(p V ~q) T T F T F T F T T F F T F F T F F T T F confidence assessment: 1
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18:29:15 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 --> correct self critique assessment: 3
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