Check my work, please? Let A, B, and C be sets. Show that
(B − A) ∪ (C − A) = (B ∪ C) − A.
Using Identities and Laws

Question

Check my work, please? Let A, B, and C be sets. Show that
 (B − A) ∪ (C − A) = (B ∪ C) − A.
Using Identities and Laws

anonymous · Answer

Assertion	Assertion
x ∈ [(B – A)∪ (C – A)]
⇔x ∈[(B ∩ A ̅ )  ∪ (C ∩ A ̅ )]	Definition of a Complement
⇔[x ∈(B ∩ A ̅ )] ∨ [x ∈(C ∩ A ̅ )]	Deﬁnition of union
⇔[x ∈(B ∧ A ̅ )] ∨ [x ∈(C ∧ A ̅ )]	Deﬁnition of intersection

⇔[x ∈(B ∨ C )]∧[x ∈ A ̅]	Distributive Law
⇔[x ∈(B ∪ C )]∩[x ∈ A ̅]	Deﬁnition of intersection

⇔x ∈[(B ∪ C )- A]	Definition of a Complement 

Looks good?