Register to reply

Stupid question related to proof writing.

by Salt
Tags: proof, stupid, writing
Share this thread:
Salt
#1
Oct22-06, 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)?
Attached Images
File Type: png Clipboard01.png (2.2 KB, 20 views)
Phys.Org News Partner Science news on Phys.org
NASA team lays plans to observe new worlds
IHEP in China has ambitions for Higgs factory
Spinach could lead to alternative energy more powerful than Popeye
HallsofIvy
#2
Oct22-06, 06:31 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,310
(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?
matt grime
#3
Oct22-06, 07:35 AM
Sci Advisor
HW Helper
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.

Salt
#4
Oct22-06, 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 :
  • there exist a x such that it's a member of F and true for P(x)

right side of 4) asserts :
  1. there exist a x such that it's a member of F and true for P(x) , or
  2. there exist a x such that it's NOT a member of F and true for P(x) , or
  3. there exist a x such that it's NOT a member of F and NOT true for P(x)

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.
Attached Images
File Type: png Clipboard0.png (11.0 KB, 2 views)
matt grime
#5
Oct22-06, 11:15 AM
Sci Advisor
HW Helper
P: 9,398
A=>B is precisely "B or not(A)".


Register to reply

Related Discussions
Transition to Proof Writing Academic Guidance 10
No such thing as a stupid question, just stupid.. Special & General Relativity 5
Basic proof writing and induction General Math 8
Stupid question looking for stupid answer Astronomy & Astrophysics 6
A stupid question by a stupid person General Physics 3