Use algebra of sets to prove that, [(𝐵 − 𝐴)' ∩ 𝐴] − 𝐴' = 𝐴

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Solution:

$LHS=[(𝐵 − 𝐴)' ∩ 𝐴] − 𝐴' \\=[(𝐵' − 𝐴')∩ 𝐴] − 𝐴'$

$=[(𝐵' − 𝐴') ∩ 𝐴] ∩ [𝐴']' \ \ [\because P-Q=P∩Q']$

$=[(𝐵' − 𝐴') ∩ 𝐴] ∩ A \\=(𝐵' − 𝐴') ∩ 𝐴∩ 𝐴 \\=(𝐵' − 𝐴') ∩ 𝐴$

$\\=(𝐵 − 𝐴)' ∩ 𝐴 \\=A-(B-A) \\=A \\=RHS$

Hence, proved.