can you prove the converse and inverse are logically equivalent?
ok - now I got it!!!
My mistrake was that I assumed the headings in both the tables were the same!!
And of course they are not!
You all saw the difference in the headings - I did not - I just assumed that I had the same headings! A very very stupid mistake.
Anyway just to conclude this thread - re-reading the definitions helped be realize my mistake.
converse: q -> p
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the hypothesis and the conclusion switch places -- the conclusion becomes the hypothesis, the hypothesis becomes the conclusion
inverse: not p -> not q
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negate both the hypothesis and the conclusion
contrapositive
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(a combination of the converse and the inverse): not q -> not p
negate and switch the hypothesis and the conclusion
Thanks for your help - I got there eventually.
Jason
yep, i think so too.
I have actually started to blog everything for dummies (i.e me) while I go along Jasoninclass's Blog
Based on the definition of =>, of course. a=> b is true in all cases except when a is true and b is false. That means that ~Q=> ~P is true in all cases except the on where ~Q is true (i.e. Q is false) and ~P is false (i.e. P is true). If you look at the last column you will see "1" ("true") in all rows except the one where P= 1 (P is true) and Q= 0 (Q is false).
By the way, have you realized that you started by talking about "not p => not q" which is certainly NOT the contrapositive you are now talking about "not q=> not p".
Hallsofivy, many thanks for your feedback at this.
I got there eventually - I realized the mistake I was making at the end of the day and documented it earlier on in the thread.
Thanks!