Prove, for all sets A, B, that A ∪ (A ∩ B) = A. You can do this by proving the following two inclusions:
A ∪ (A ∩ B) ⊆ A and A ⊆ A ∪ (A ∩ B).

Question

Prove, for all sets A, B, that A ∪ (A ∩ B) = A. You can do this by proving the following two inclusions:
A ∪ (A ∩ B) ⊆ A and A ⊆ A ∪ (A ∩ B).

jango_in_dtown · Answer

Hi may I help you?

jango_in_dtown · Answer

@Bee_see

jango_in_dtown · Answer

Let x belongs to A ∪ (A ∩ B)
Then x belongs to A or x belongs to A∩ B
Hence in either case x belongs to A.
Therefore x belongs to  A ∪ (A ∩ B) implies x belongs to A 
Therefore A ∪ (A ∩ B) ⊆ A.
Now let y belongs to A.
Then obviously y belongs to A∪ (A ∩ B)
Hence A ⊆ A ∪ (A ∩ B).
In other words A ∪ (A ∩ B) = A

bee_see · Answer

Sorry...I didn't get a notification. When you say, x belongs to A or x belongs to A and B., are you taking about the A's on the left side or right side?