1.

if a b c are any three sets then a-(buc) is equal to

Answer» Jjddkd<br>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 ∩ C)⇒ x ∈ A and (x ∉ B or x ∉ 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 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 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) ∪ x ∈ (A - 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) ∪ x ∈ (A - C)∴ A - (B ∩ C) ⊆ (A - B) ∪ (A - 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) ∪ x ∈ (A - C)∴ A - (B ∩ C) ⊆ (A - B) ∪ (A - C)Similarly, (A - B) ∪ (A - C) ⊆ 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) ∪ x ∈ (A - C)∴ A - (B ∩ C) ⊆ (A - B) ∪ (A - C)Similarly, (A - B) ∪ (A - C) ⊆ A - (B ∩ C)Hence, A - (B ∩ C) = (A - B) ∪ (A - C)Step-by-step explanation:HOPE THIS WILL HELP YOUTHANKS?


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