course Mth 151 Cv۶㝍ߥizЅassignment #014
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09:37:16 3.3.6 rewrite using if then ' all marines love boot camp '.
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RESPONSE --> If it is boot camp, then all Marines love it confidence assessment: 3
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09:37:22 ** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent. The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. **
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RESPONSE --> OK self critique assessment: 3
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09:38:04 3.3.18 ~p false q false p -> q true
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RESPONSE --> p -> q is of the form T -> F, which is false confidence assessment: 3
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09:38:09 ** Since ~p is false then p is true. Since q is false it follows that p -> q is of the form T -> F, which is false. The conditional is false when, and only when, the antecedent is true and the consequent false. **
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RESPONSE --> OK self critique assessment: 3
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09:38:31 Query 3.3.36 write in symbols 'If play canceled, then it does not rain.'
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RESPONSE --> p -> ~q confidence assessment: 3
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09:38:36 ** If p stands for 'play canceled' and r for 'it rains' then the statement would be p -> ~q. **
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RESPONSE --> OK self critique assessment: 3
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09:39:01 Query 3.3.48 q true, p and r false, evaluate and (-r U p) -> p
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RESPONSE --> The antecedent (~r U p ) would be true, since ~r true and p false. The consequent p would be false. Since the antecedent is true and the consequent false, the conditional is false. confidence assessment: 3
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09:39:14 ** The antecedent (~r U p ) would be true, since ~r true and p false. The consequent p would be false. Since the antecedent is true and the consequent false, the conditional is false. **
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RESPONSE --> OK self critique assessment: 3
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09:39:59 Query 3.3.60 truth table for (p ^ q) -> (p U q)
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RESPONSE --> 1 T T T T T 2 T F F T T 3 F T F T T 4 F F F F T confidence assessment: 2
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09:40:27 ** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq) Row 1 would read T T T T T Row 2 would read T F F T T Row 3 would read F T F T T Row 4 would read F F F F T The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q). The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. **
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RESPONSE --> I forgot to evaluate the statement, but I am happy with my grasping of the truth tables. self critique assessment: 2
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09:41:16 Query 3.3.72 negation of ' if loving is wrong then I don't want to be right'
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RESPONSE --> If loving you is wrong, then I want to be right confidence assessment: 3
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09:41:55 ** The negation has to have the exact opposite truth values of the original statement. It is difficult and confusing to try to negate a conditional. It is much easier to translate the conditional to a disjunction then negate the disjunction. It is easy to negate the disjunction using deMorgan's Laws. Since p -> q is identical to ~p U q, the negation of p -> q is ~ ( ~p U q), which by de Morgan's Law is ~ ~p ^ ~q, or just p ^ ~q. So the negation would ge 'loving you is wrong AND I want to be right. COMMON ERROR AND NOTE: If loving you is wrong, then I want to be right. INSTRUCTOR COMMENT: The negation of a conditional can't be a conditional (a conditional is false in only one case so its negation would have to be false in three cases). **
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RESPONSE --> I realize that the negotions would have to be false in three cases, I didn't think deep enough into the problem self critique assessment: 3
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09:42:38 Query 3.3.90 circuit q parallel [ p in series with ( q par. ~p) ].
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RESPONSE --> q U [ p ^ [q U ~p ] confidence assessment: 3
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09:42:48 ** If I'm looking at the same circuit you are the translation would be q U [ p ^ [q U ~p ]] . Since intersection and union each distribute over the other, this would simplify to q U [ ( p ^ q) U ( p ^ ~p) ]. Since p ^ ~p can't be true, this is the same as q U ( p ^ q). Since q U ( p ^ q) is true whenever q is true and false whenever q is false expression is true exactly when q is. So the circuit finally simplifies to just q. You should be able to see by looking at the circuit that current will flow whenever all the q switches are closed. **
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RESPONSE --> OK self critique assessment: 3
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