
#1
Oct2206, 04:38 AM

P: 15

I have no idea how to type math symbols into here so it's all in the PNG attached.
I'm probably kind of dumb for not getting this but... I understand that 1) & 3) are true. And the 2) is not right, as it means all x are members of F and true for P(x) when we mean all x that are members of F are true for P(x). But why do we use 3) instead of 4)? 



#2
Oct2206, 06:31 AM

Math
Emeritus
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Thanks
PF Gold
P: 38,882

(4) is not always a true statement. The right hand side of (4) would be true even if F were empty whereas the left hand side would not be. Notice that if x is NOT in F then "x contained in F implies P(x)" is a TRUE statement because the hypothesis is FALSE.
matt, that was pretty much what you said. Why did you delete it? 



#3
Oct2206, 07:35 AM

Sci Advisor
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P: 9,398

Cos when I looked more closely I decided that I couldn't decipher the small subscript on the LHS with any certainity.




#4
Oct2206, 10:07 AM

P: 15

Stupid question related to proof writing.
Thanks everyone. Sorry about the size, I attached a bigger one in this post.
So from what I understand from reading the replies and scratching my head over the AND and IMPLIE truth tables. right side of 3) asserts :
right side of 4) asserts :
However we do not wish to state as true 2. and 3. , for it would implie that there exist a x that is NOT a member of F. As the set representing "not F" may or may not be empty. Anyway that's the reasoning I manage to arrive at. 



#5
Oct2206, 11:15 AM

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P: 9,398

A=>B is precisely "B or not(A)".



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