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fallacy

can some 1 help me wid this question


Consider each of the following arguments. If the argument is valid, identify the rule of inference that establishes its validity. If not, provide a statement that demonstrates the fallacy in the reasoning:


Q: If I eat cheese I will get a migraine. If I get a migraine I will have to take a day off work. Therefore, if I eat cheese I will have to take a day off work.

my attamt

p to Q
q to r
-----------------
.. p to R
.

and then a truth table based on this calculation.
Reply 1
Avatar for Kolya
Kolya
17
Use the transitivity of logical implication: If A  ⟹  BA \implies B and B  ⟹  CB \implies C then A  ⟹  CA \implies C.

If you need to draw a truth table then the statement you have to draw it for is: ((A  ⟹  B)∧(B  ⟹  C))  ⟺  (A  ⟹  C)((A \implies B) \land (B \implies C)) \iff (A \implies C) If the   ⟺  \iff column then consists only of "True" truth-values, the statement is a tautology and we conclude the argument in question is valid.
Reply 2
Avatar for Chewwy
Chewwy
17
transitivity my dear watson.
Reply 3
Avatar for Zhen Lin
Zhen Lin
12
It is indeed transitivity. If a relation ~ is such that a ~ b and b ~ c implies a ~ c then ~ is transitive.
Reply 4
Avatar for Kolya
Kolya
17
Chewwy
transitivity my dear watson.
Jolly good.
Reply 5
Avatar for Cexy
Cexy
Lusus Naturae
If you need to draw a truth table then the statement you have to draw it for is: ((A  ⟹  B)∧(B  ⟹  C))  ⟺  (A  ⟹  C)((A \implies B) \land (B \implies C)) \iff (A \implies C) If the   ⟺  \iff column then consists only of "True" truth-values, the statement is a tautology and we conclude the argument in question is valid.


Not quite true. All that you want to show is valid is the statement:

"IF ((A  ⟹  B)∧(B  ⟹  C))((A\implies B)\land(B\implies C)) THEN (A  ⟹  C)(A\implies C)"

All that you need to show to establish that the statement "IF P THEN Q" is true is that Q is true whenever P is true, and P is false whenever Q is false.
Reply 6
Avatar for Kolya
Kolya
17
Cexy
Not quite true. All that you want to show is valid is the statement:

"IF ((A  ⟹  B)∧(B  ⟹  C))((A\implies B)\land(B\implies C)) THEN (A  ⟹  C)(A\implies C)"

All that you need to show to establish that the statement "IF P THEN Q" is true is that Q is true whenever P is true, and P is false whenever Q is false.
Thanks for the correction. :smile:
Reply 7
Avatar for Miss Nash
Miss Nash
OP
1
thanksssssssssssssssssssss

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