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if a b c are any three sets then a-(buc) is equal to
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❤️Ritesh Gupta? 3 years, 5 months ago

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Gurleen Singh 3 years, 5 months ago

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 YOU THANKS?
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