If A,B and C are any three sets ,then A multiply ( B union C ) is equal to what?
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The proof is explained step wise below :
Step-by-step explanation:
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) ∪ 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:
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