#$&* course Mth 151 014. `query 14
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Given Solution: `a** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent. The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q3.3.18 ~p false q false p -> q true YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: ~p being false makes it true q is just false T -> F, which is a false statement confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 2 ********************************************* Question: `qQuery 3.3.36 write in symbols 'If we don't bike, then it does not rain.' YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: ~p -> ~q confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~r. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I don’t understand why “we don’t bike” is just p and not ~p. Wouldn’t the negation of “we don’t” be “we do”??? ------------------------------------------------ Self-critique Rating: 1
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Given Solution: `a** The antecedent (~r U p ) would be true, since ~r true and p false. The consequent p would be false. Since the antecedent is true and the consequent false, the conditional is false. ** MORE DETAILED SOLUTION r is said to be false, so ~r is true p is said to be false Therefore the disjunction (~r U p) would be a disjunction of a true and a false statement. A disjunction is true if at least one of the statements is true, so (~r U p) is true. The conditional (~r U p) -> p therefore consists of an antecedent which is true, and a consequent which is false. By the rules for a conditional, the statement is therefore false. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 2 ********************************************* Question: `qQuery 3.3.60 truth table for (p ^ q) -> (p U q) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: p q (p ^ q) (p U q) (p ^ q) -> (p U q) T T T T T T F F T T F T F T T F F F F T confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK. True tables have been giving me a lot of problems so I’m very excited to know I understood one, finally. ------------------------------------------------ Self-critique Rating: 3
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Given Solution: `a** 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). ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I understand how negation works but I didn’t consider the “and” ------------------------------------------------ Self-critique Rating: 2 " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!