Let us take an example to prove it.

Let A = {2, 4, 6, 8, 10} and B = {1, 2, 3, 4, 5}

1. A ∩ B = {2, 4}

A - B = {6, 8, 10}

Now, (A ∩ B) ∪ (A - B) = {2, 4, 6, 8, 10}

So, A = (A ∩ B) ∪ (A - B)

2. B - A = {1, 3, 5}

A ∪ (B - A) = {1, 2, 3, 4, 5, 6, 8, 10}

and A ∪ B = {1, 2, 3, 4, 5, 6, 8, 10}

 So, A ∪ (B - A) = A ∪ B