Hello,

Can someone please help me with this proof?

(A-C)∩(C-B) = 0.

Do I start off by....

suppose: ~[(A-C)∩(C-B) = 0.] ?

Also, does this (0 ∩ B') equal the empty set?

Thanks...

PS. ' indicates the complement.

Printable View

- May 7th 2010, 11:08 PMl flipboi lProof By Contradiction
Hello,

Can someone please help me with this proof?

(A-C)∩(C-B) = 0.

Do I start off by....

suppose: ~[(A-C)∩(C-B) = 0.] ?

Also, does this (0 ∩ B') equal the empty set?

Thanks...

PS. ' indicates the complement. - May 7th 2010, 11:24 PMtonio
Why not start by the mere definition? Suppose $\displaystyle x\in\left(A-C\right)\cap\left(C-B\right)\Longrightarrow x\in A-C\,\,\,and\,\,\,also\,\,\,x\in C-B$ ...from here the way to get a contradiction is straightforward and thus no such element can exist...

Tonio - May 7th 2010, 11:37 PMl flipboi l
Thats exactly what I did, i'm not sure if I did it correctly though.

This is what I got :

(A ∩ 0) ∩ B'

(0 ∩ B')

0

is that correct? - May 8th 2010, 12:52 AMtonio
- May 8th 2010, 12:56 AMl flipboi l
- May 8th 2010, 01:05 AMtonio
- May 8th 2010, 01:29 AMl flipboi l
Thanks for the help! I meant, I set it up like how you did.