Answer to Question #195944 in Discrete Mathematics for zaynab

Question

Let A, B, and C be sets. Show that (B − A) ∪ (C − A) = (B ∪ C) – A by using Venn diagram?                                                   

Answer 1

Left Hand Side:

$(B-A)\cup(C-A)$

$(B-A):$

$(C-A):$

So,

$(B-A)\cup(C-A)$ :

Right Hand Side:

$(B\cup C)-A$

$(B\cup C):$

and

$(B\cup C)-A:$

So, from Venn Diagram, it is clear that

$\boxed{(B-A)\cup (C-A)=(B\cup C)-A}$