Theorem 2
Theorem 2 If A,B and C are any three sets,then prove that:

$(i) A - (B \cap C) = (A - B) \cup (A - C) (ii) A - (B \cup C) = (A - B) \cap (A - C) (iii) A \cap (B - C) = (A \cap B) - (A \cap C) (iv) A \cap (B △ C) = (A \cap B) △ (A \cap C)$

Question

Theorem 2
Theorem 2 If A,B and C are any three sets,then prove that:

i   A - B ∩ C = A - B ∪ A - C ( ii )   A - ( B
∪ C ) = A - B ∩ A - C ( iii )   A ∩ B - C = A
∩ B - ( A ∩ C ) ( iv )   A ∩ B △ C = A ∩
B △ A ∩ C

Neha Sethi · Accepted Answer

Dear student (i) Let x be any element of A-B∩C Then,x∈A-B∩C⇒x∈A and x∉B∩C⇒x∈A and (x∉B or x∉C)⇒x∈A and x∉B or x∈A and x∉C ⇒x∈(A-B) or x∈(A-C)⇒x∈(A-B)∪(A-C)∴ A-B∩C⊆A-B∪A-CSimilarly,A-B∪A-C⊆A-B∩CHence, A-B∩C=A-B∪A-C

Regards

Theorem 2 Theorem 2 If A,B and C are any three sets,then prove that: i A - B ∩ C = A - B ∪ A - C ( ii ) A - ( B ∪ C ) = A - B ∩ A - C ( iii ) A ∩ B - C = A ∩ B - ( A ∩ C ) ( iv ) A ∩ B △ C = A ∩ B △ A ∩ C

Theorem 2
Theorem 2 If A,B and C are any three sets,then prove that:

$(i) A - (B \cap C) = (A - B) \cup (A - C) (ii) A - (B \cup C) = (A - B) \cap (A - C) (iii) A \cap (B - C) = (A \cap B) - (A \cap C) (iv) A \cap (B △ C) = (A \cap B) △ (A \cap C)$