Question:
For all sets A and B, (A – B) ∪ (A ∩ B) = A
Solution:
True
According to the question,
There are two sets A and B
To check: (A – B) ∪ (A ∩ B) = A is true or false
L.H.S = (A – B) ∪ (A ∩ B)
Since, A – B = A ∩ B’,
We get,
= (A ∩ B’) ∪ (A ∩ B)
Using distributive property of set:
We get,
(A ∩ B) ∪ (A ∩ C) = A ∩ (B ∪ C)
= A ∩ (B’ ∪ B)
= A ∩ U
= A
= R.H.S
Hence, the given statement “for all sets A and B, (A – B) ∪ (A ∩ B) = A” is true