# Thread: Subsets that have a disjoint

1. ## Subsets that have a disjoint

How can I prove this:
$If A \subset B\cup C$ and A and B are disjoint, the $A \subset C.$

2. Originally Posted by tigergirl
How can I prove this:
$If A \subset B\cup C$ and A and B are disjoint, the $A \subset C.$
If $A~\&~B$ are disjoint then $x \in A~ \Rightarrow ~ x\notin B$.

3. after you answer your question in your other post, this follows directly from that - just write down the definition of disjoint sets, which is that their intersection is the empty set.