Are you sure that these sets are different ? in fact
Let
if and therefore
else (since )
therefore
Hey guys, I am working on this proof which I initially thought was true, but found a contradiction while working through it, so I am pretty sure that the statement is false.
However, if its false, I need to find an example for which its false and that is what I am having trouble with. I just cant seem to pick the right numbers.
Statement:
For all sets A, B, C (A-B) U (B-C) = (AUB) - (B (intersect) C)
Haha sorry, I dont know how to make an upside down U, so I just wrote intersect.
Also, is there any method to picking sets that give you a counter example? or is it just blind guessing?
So this is my proof that the statement is actually true, correct me if I am wrong.
(AUB)-(B∩C)
x: xεA v xεB ^ ~xεB v ~xεC [by demorgans law]
xεA ^ ~xεB v xεB ^ ~xεC
(A-B)v(B-C) [by set difference law]
I am not really sure what law would the 2nd line be but I believe this to be correct..
Tah you have nearly completed the proof without realizing that:
WE want to prove :
first and then
Let
And:
.................................................. ........................................1
.................................................. .....................................2
Now let .................................................. ........................................3
But from (1) we have : .................................................. .........................................4
And from (3) and (4) we get:
.................................................. .......5
But from (2) we have: .................................................. ..........6
And from (5) and (6) we have: ..................................7
Combining (5) and (7) we have:
Finally we have proved:
.
Hence ,
To prove the converse is not so difficult