course Mth 151
7/12 1
Question: `qQuery 3.6.5 if he didn't have to set up he would be ecstatic. He's ecstatic. Therefore he doesn't have to set up.
Is the argument and valid or invalid and why?
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Your solution:
Not valid because we know that he is ecstatic if he doesn’t have to set up but this doesn’t mean since he is ecstatic he doesn’t have to set up it is a contradiction
3
Ok
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Question: `qQuery 3.6.11 (formerly 3.6.12). This wasn't assigned but you should be able to analyze it. {}{}She uses ecommerce or uses credit. She doesn't use credit. Therefore she uses ecommerce. {}{}Is the argument and valid or invalid and why?
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Your solution:
Valid because she only uses one or the other therefore if she doesn’t use one she must use the other
3
Ok
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Question: `qQuery 3.6.18 evaluate using the truth table: ~p -> q, p, therefore -q
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Your solution:
p q ~p ~q (p--> ~q) {(p--> ~q) ^ ~p} {(p--> ~q) ^ ~p} --> ~q
T T F F F F T
T F F T T F T
F T T F T T F
F F T T T T T
2
Ok
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Question: `q3.6.24 evaluate using the truth table: ( (p ^ r) -> (r U q), and q ^ p), therefore r U p
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Your solution:
pqr r^p q^p rUp rUq (r^p)->(rUq) [(r^p)->(rUq)]^(q^p) {[(r^p) -> (rUq)] ^ q^p} -> rUp
ttt t t t t t t t
ttf f t t t t t t
tft t f t t t f t
tff f f t f t f t
ftt f f t t t f t
ftf f f f t t f t
fft f f t t t f t
fff f f f f t f t
All T's in the last column show that the argument is valid.
2
Ok
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Question: `q3.6.30: Christina sings or Ricky isn't an idol. If Ricky isn't an idol then Britney doesn't win. Britney wins. Therefore Christina doesn't sing.
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Your solution:
This is valid because Britney won means Ricky is an idol therefore Christina doesn’t sing
3
Ok
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Question: `qPrevious version 3.6.30 determine validity: all men are mortal. Socrates is a man. Therefore Socrates is mortal
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Your solution:
r -> p
p -> q
therefore
r -> q
The final column would come out with all T's, proving the validity of the argument
3
Ok
"
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