#$&* course Mth 151 05/06/20111205 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `a** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent. The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):N/A ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `q3.3.18 ~p false q false p -> q true YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: THIS WOULD BE FALSE. TO BE TRUE IT WOULD NEED TO BE ~P FALSE Q TRUE confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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):N/A ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `qQuery 3.3.36 write in symbols 'If we don't bike, then it does not rain.' YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: ~R > ~B confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~r. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): N/A * BOOK CLAIMS THAT B REPRESENTS THE ‘I LIKE MY BIKE’ AND IN THE GIVEN SOLUTION P IS USED AND THAT REPRESENTS ‘THE CONCERT IS CANCELLED ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `qQuery 3.3.48 q true, p and r false, evaluate (-r U p) -> p YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (R V P) -> P confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): N/A ------------------------------------------------ Self-critique Rating:3 ********************************************* Question: `qQuery 3.3.60 truth table for (p ^ q) -> (p U q) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: IT WOULD READ AS THE FOLLOWING: TTTTT / TFFTT / FTFTT / FFFFT confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): DO WE NEED TO PUT THE HEADINGS ON THE TRUTH TABLES?
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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 DID THE COMMON MISTAKE. I UNDERSTAND WHY YOU DO NOT USE THEN AND USE AND ------------------------------------------------ Self-critique Rating:3 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!