Prove: If A and B are disjoint and B and C are disjoint so $Acup C$ and B are disjoint
We know that $Acap B=emptyset wedge Bcap C=emptyset rightarrow (Acap B)cap (Bcap C)= emptyset rightarrow (Acap B)=emptyset wedge (Bcap C)= emptyset$
On the other hand $(Acup C)cap B= emptyset rightarrow (Acap B)cup (C cap B)=emptyset rightarrow (Acap B)=emptyset vee (Ccap B)=emptyset$
How can I prove it?