Question

Q1. If A,B and C are any three sets, then A-(BUC)=
1) (A-B) n ​

Answer 1

Answer:

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: