Question:
For all sets A and B, A ∪ (B – A) = A ∪ B
Solution:
According to the question,
There are two sets A and B
To prove: A ∪ (B – A) = A ∪ B
L.H.S = A ∪ (B – A)
Since, A – B = A ∩ B’, we get,
= A ∪ (B ∩ A’)
Since, distributive property of set ⇒ (A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C), we get,
= (A ∪ B) ∩ (A ∪ A’)
Since, A ∪ A’ = U, we get,
= (A ∪ B) ∩ U
= A ∪ B
= R.H.S
Hence Proved