For all sets A and B,

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

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