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

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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

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

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Question ID: mtid-5-stid-8-sqid-2980-qpid-1679