2. Smoking causes cancer
I smoke cigarettes
-------------------
Therefore, I have lung cancer
3.
4. This argument would be invalid and true. Most lung cancer patients smoke, but I smoke and do not have lung cancer.
5. If I smoke cigarettes, then I have lung cancer
p: I smoke cigarettes
q: I have lung cancer
if p and q, then q
( p ^q ) -> q
6.
a/b. This statement is not a tautology, that makes sense because not all smokers develop lung cancer, however lung cancer is still very common in smokers.
c. Truth tables are useful in determining if an argument is a valid tautology.
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ReplyDeleteGood topic! Although I think (I may be wrong) but that the venn diagram could be one that has a shared intersection instead of having all lung cancer patients smoke because that is not always true. Some lung cancer patients get it from somewhere else such as genes :)
ReplyDeleteI agree but I think that it may be valid but untrue. You could still get lung cancer with out smoking cigarettes
ReplyDeleteNice argument! We did the same one!
ReplyDeleteNice argument! We did the same one!
ReplyDeletecarson,
ReplyDeletegood topic for this blog entry. it's definitely relevant in our day and age. i feel like this argument would be INVALID and untrue, based on the explanation that you give regarding the fact that YOU smoke, but don't have lung cancer. wouldn't that mean that this statement is not necessarily true since you are a counterexample? that said, the arrow that you used to indicate where you are in the venn diagram should be INSIDE the smaller circle. the argument that you have written is in the "all a are b, x is a, x is b" from, hence it is valid. however, it is not true. additionally, i am a tad confused on the labeling of your truth table and its results.
i do love how organized and polished looking your post is. nice job. all in all, though, a good post.
professor little