IF A, B and C are sets. Then A/B is a subset of C if and only if A/C is a subset of B. I need to create a proof for this and I am lost on how to go about it,

Question

IF A, B and C are sets. Then A/B is a subset of C if and only if A/C is a subset of B.   I need to create a proof for this and I am lost on how to go about it,

anonymous · Answer

what does A/B mean?

anonymous · Answer

In SET A less SET B

anonymous · Answer

i wonder if a picture would help

anonymous · Answer

I tried a picture...I have done by assigning values to each set and made it work

anonymous · Answer

my picture makes it seem like it is not true
maybe we can come up with an easy counter example

anonymous · Answer

Set A {1,2,3,4}   SET B = {3}  Thus Set A/B is  {1,2,4}   Now make that SET C {1,2,4)

So Set A=  {1,2,3,4}  Set C = {1,2,4}  Then A/C = {3} which is a subset of B

anonymous · Answer

maybe we can try this 
Assume $A\cap B^c\subset C$ and pick an $x\in A\cap C^c$  and show that $x$ must be in $B$ 
if not , then $x\in B^c$ and so in $A\cap B^c$  which you know by assumption is contained in $C$ contradicting it being in $A\cap C^c$

anonymous · Answer

no didn't 
i just wrote $A\cap B^c$ instead of A/B

anonymous · Answer

I have x is an element of A and x is not and element of B is a Subset of C.

anonymous · Answer

right that is what i wrote with $A\cap B^c\subset C$

anonymous · Answer

is it clear how to structure this proof? you have to assume that $A\cap B^c\subset C$ then pick an $x\in A\cap C^c$ and show that it is in $B$ 
that will prove that $A\cap C^c\subset B$

zarkon · Answer

Does anyone actually use A/B for set minus (I don't have any books that do this...and I have a lot of books)

the usual notation is A\B or A-B