Stupid question related to proof writing.


by Salt
Tags: proof, stupid, writing
Salt
Salt is offline
#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's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
HallsofIvy
HallsofIvy is offline
#2
Oct22-06, 06:31 AM
Math
Emeritus
Sci Advisor
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?
matt grime
matt grime is offline
#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
Salt is offline
#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
matt grime is offline
#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 General Astronomy 6
a stupid question by a stupid person General Physics 3