Sample Exam I key
Sample Exam I key
1) True 2) False 3) True 4) False 5) False
6) A sound argument is one which is both VALID and has all true premises. Since a valid argument is one in which the truth of the premises guarantees the truth of the conclusion, it follows that the conclusion of a sound argument MUST be true. So, any argument with a false conclusion is unsound.
7) I would use a consistency checker to test for validity in the following way. We know that in a valid argument it is impossible for the premises to be true while the conclusion is false. Accordingly, the set {all true premises, false conclusion} must be inconsistent. SO, I would run the set of statements {all true premises, false conclusion} through the consistency checker. If that set is consistent, the argument is non-valid. If the set is inconsistent, then the argument is valid.
8) True
[ |( |P |( |R |) |v |Q |] |v |( |R |v |~ |Q |) | | | |F | |? | | |T | | | |? | | |T | | | | | |F | | | | | | | |? | |F | | | | | | | | | |T | | | | | |? | | | | | | | | | | | | | |T | | | | | | | |
9) True
( |P |v |Q |) |( |( |~ |Q |( |~ |P |) | | |F | |T | | | | |T | | |F | | | | |T | | | | |F | | |T | | | | | | | | | | | | |T | | | | | | | | | |T | | | | | | | | |
10) True
11) (~C ( ~S) ( (~I ( D)
12) (B v F) ( G
13) (D ( R) ( (H v P)
14) Truth table for formula 12
B |F |G | |( |B |v |F |) |( |G | |T |T |T | | | |T | | |T | | |T |T |F | | | |T | | |F | | |T |F |T | | | |T | | |T | | |T |F |F | | | |T | | |F | | |F |T |T | | | |T | | |T | | |F |T |F | | | |T | | |F | | |F |F |T | | | |F | | |T | | |F |F |F | | | |F | | |T | | | | | | | | | | | | | | |
15)Not Equivalent—ROWS 1 AND 2 DISAGREE IN TRUTH VALUE
P |Q | |~ |P |v |Q | |~ |( |P |( |Q |) | |T |T | |F | |T | | |F | | |T | | | |T |F | |F | |F | | |T | | |F | | | |F |T | |T | |T | | |T | | |F | | | |F |F | |T | |T | | |T | | |F | | | | | | | | |** | | |** | | | | | | |
16) Valid
17) Not consistent, it is impossible to make all three claims true. For the last to be true, P must be true and R false. No matter what value is assigned to Q, either the first or the second claim will be false.
18)Valid, you cannot make the premises true and the conclusion false
19)Valid
P |( |Q | |~ |P |( |R | |R |v |Q | | | | | | | | | | | |F | |F |first step, make the conclusion false | | | | | | | | | | | |F | | | | | |F | | | | |F | | | | |plug in the assumptions made above | |
F | |
F | | | | | | | | | |attempt to make the premises true
start anywhere | | |T | | | | | | | | | | |if P is false, premise 1 is true | | | | | | |F | | | | | | | | | | | | |T | | |F | | | | |However, if P is false, ~P is true | | | | | | | |F | | | | | |and a conditional with a true antecedent and a false consequent is false | | |T | | | | |F | | | |F | |Since it is impossible to make the premises true and the conclusion false, the argument is valid | |
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