Let A, B and C be sets. Prove that

[iHeartof12]

*Sorry wrong section*
Let A, B and C be sets.
Prove that if A\subseteqB\cupC and A\capB=∅, then A\subseteqC.

My attempted solution:
Assume A\subseteqB\cupC and A\capB=∅.
Then \veex (x\inA\rightarrowx\inB\cupx\inc).

I'm not sure where to start and how to prove this. Any help would be greatly appreciated. Thank you.

 

[jedishrfu]

you almost have it.

for all x in A and A is a subset of B U C then x is in B U C
if x is in B U C then x is in B or x is in C

now just describe x with respect to the A \bigcap B = ∅

 

[Bacle2]

Another perspective: you can maybe rigorize it by saying:

a in B or a in C , but a not in B , so we must have a in C:

Basically, as you rightly concluded, a must be in one

of B or C, but ,by assumption/construction, a is not in B,

so a must be in C.