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option (i)  iam not sure  but let  r = (a+b)  

L(a+b)* = { Ɛ ,a ,b, ab, ba ,abb ,.......}     = LHS

RHS = ( L(R) ) *  = ( a+b)*  there fore LHS  = RHS it holds

(ii) $(a^+ + \phi ^*)^* = (a^+ + \phi )^*$

= $(a^+ + \epsilon )^* = ( a^+)^*$

=$(a^*)^* = (a)^*$

hence it holds 

(iii) $(a^+)^* = (a^*)^+$ 

holds always as $(R^*)^+ = (R^+)^*$

(iv)  $(a^+ + \phi^* )^+ = (a^+ + \phi )^*$

 $(\epsilon +a^+)^+ = (a^+)^*$

$(a^*)^+ = (a^+)^*$

hold true 

Therefore , All options correct 

  remember  $\phi + R = R$

and $\epsilon + R^+ = R^*$

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