Consider the following identities for regular expressions; some are false and some are true. Decide which and in case it is false to provide the correct counterexample.

(a) R(S+T)=RS+RT

(b) (R*)*=R*

(c) (R*S*)*=(R+S)*

(d) (R+S)*=R*+S*

(e) S(RS+S)*R=RR*S(RR*S)*

(f) (RS+R)*R=R(SR+R)*

a) (d) is false and a counterexample is:

R={ab},T={a}, S={b}

b) (c) is false and a counterexample is:

R={ab},T={b}, S={b}

c) (e) is true

d) (e) is false and a counterexample is:

R={a,},T={b}, S={a,}

What is the answer? Explain please