sandii2006
Write the argument below in symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q you used. Submit your full detailed solution
If the koi are swimming in the pond, then the birds are chirping.
The birds are not chirping.
The koi are not swimming in the pond.
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hahd
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birds are dependent on koi swimming
hahd
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if koi dont swim then birds dont chirp
101Ryan101
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If the Packers are playing, koi might be swimming.
Dangolbery
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koi only swims on sundays
sandii2006
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come on guys i'm trying to LEARN THIS please.... no joking around.. I would appreciate it..
jim_thompson5910
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p: the koi are swimming in the pond
q: the birds are chirping
So the argument translates to
p --> q
~q
.: ~p
So this is a valid argument since it uses the Modus Tollens form
snaef999
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if k = s then b = c
b != c thus k!=s
abtrehearn
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\[p \rightarrow q\]not p
therefore, not q.
The argument is valid [contrapositive]
sandii2006
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how come you both got DIFFERENT answers?
jim_thompson5910
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abtrehearn is using not p instead he should be using not q
hahd
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p --> q
~q
.: ~p
jim_thompson5910
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but the law of the contrapositive is another way to say modus tollens
sandii2006
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ok which is the "correct" way to say it jim?
jim_thompson5910
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not sure which one your book uses
sandii2006
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i believe it the modus
abtrehearn
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My mistake.
jim_thompson5910
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have you seen that term before?
hahd
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jim is right
jim_thompson5910
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well you have the law of contrapositive correct (since that's just another way of saying modus tollens)
sandii2006
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yes i have seen that term before jim
jim_thompson5910
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ok then that's one way to justify your answer
abtrehearn
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Got the p and q backwards.
sandii2006
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ok thank you. for clarifying it jim :)