Let R₁ and R₂ be two regular expressions over the alphabet {a , b}

a) Is it always the case that L(((R₁).(R₂))*) = L(((R₁)|(R₂))^*)?

b) Is it always the case that L(((R₁)^*.(R₂)^*)^*) = L(((R₁)|(R₂))^*)?

c) Is it always the case that L((R₁^*)^*) = L((R₁)^*)?