course mth151 014. `query 14 ********************************************* ********************************************* Question: `q3.3.5 rewrite using if then ' all marines love boot camp '. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If it’s a marine, then it loves boot camp If it’s boot camp, then all marines love it confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
.............................................
Given Solution: `a** The statement is equivalent to 'If it's a Marine, it loves boot camp' or equivalent. The statement is not equivalent to 'if it is boot camp, then all Marines love it', which is the converse of the original statement. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique rating #$&*:2 ********************************************* ********************************************* Question: `q3.3.18 ~p false q false p -> q true YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: p is true confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
.............................................
Given Solution: `a** Since ~p is false then p is true. Since q is false it follows that p -> q is of the form T -> F, which is false. The conditional is false when, and only when, the antecedent is true and the consequent false. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):This question confuses me,
.............................................
.............................................
Given Solution: `a** If p stands for 'don't bike' and r for 'it rains' then the statement would be p -> ~r. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique rating #$&*:2 ********************************************* ********************************************* Question: `qQuery 3.3.48 q true, p and r false, evaluate (-r U p) -> p YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: the consequent false and the antecedent is true which means the conditional is false confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
.............................................
Given Solution: `a** The antecedent (~r U p ) would be true, since ~r true and p false. The consequent p would be false. Since the antecedent is true and the consequent false, the conditional is false. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique rating #$&*:2 ********************************************* ********************************************* Question: `qQuery 3.3.60 truth table for (p ^ q) -> (p U q) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: p, q ,(p^q), (pUq), (p^q)->(pUq) T T T T T T F F T T F T F T T F F F F T confidence rating #$&*: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
.............................................
Given Solution: `a** The headings would be p, q ,(p^q), (pUq), (p^q)->(pUq) Row 1 would read T T T T T Row 2 would read T F F T T Row 3 would read F T F T T Row 4 would read F F F F T The common sense of this is that whenever both p and q are true, then the statement 'p or q' must be true. That's what means to say (p ^ q) -> (p U q). The fact that this statement is true is indicated by the last column of the truth table, which has True in every possible case. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique rating #$&*:2 ********************************************* ********************************************* Question: `qQuery 3.3.74 (formerly 3.3.72). This wasn't assigned but it is similar to assigned questions and should be answered: What is the negation of the statement 'if loving you is wrong then I don't want to be right' ? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: loving you is wrong and I want to be right confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
.............................................
Given Solution: `a** The negation has to have the exact opposite truth values of the original statement. It is difficult and confusing to try to negate a conditional. It is much easier to translate the conditional to a disjunction then negate the disjunction. It is easy to negate the disjunction using deMorgan's Laws. Since p -> q is identical to ~p U q, the negation of p -> q is ~ ( ~p U q), which by de Morgan's Law is ~ ~p ^ ~q, or just p ^ ~q. So the negation would ge 'loving you is wrong AND I want to be right. COMMON ERROR AND NOTE: If loving you is wrong, then I want to be right. INSTRUCTOR COMMENT: The negation of a conditional can't be a conditional (a conditional is false in only one case so its negation would have to be false in three cases). ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique rating #$&*:2