Idempotent means if operands of your operator are equal then you should get operand as o/p
V) a+a =a
you know that a+b means either a or b ===> put a in place of b ===> a+a = either a or a = a ===> Follow idempotent Law
VI) a.a ҂ a
you know that a.b means a concatenate with b ===> put a in place of b ===> a.a = aa ҂ a ===> Doesn't Follow idempotent Law
I) (P+Q)* P* Q* ------------> every string in the language, actually you can get every string in the language by (P+Q)*
therefore (P+Q)* P* Q* = (P+Q)*
II) can be self explanatory after getting (I)
III) ∊ + R = either ∊ or R, if R contains ∊ ===> ∊ + R = R
IV) ∊ + R = R? -----------------> False
R? means R can be one time or zero
ex:- R=ab
∊ + R = { ∊ , ab}
R? = {∮, ab}
