Let us take cases one by one :
Case 1 :
LHS = R1 + R2.R3
= R1 + R1.R3
RHS = (R1 + R2) . (R1 + R3)
= R1.( R1 + R3) [ As R1 = R2 given ]
= R1 . R1 + R1 . R3 [ As follows from the distributive property ]
which is not equal to LHS as R1 . R1 != R1..Hence (i) is false..
Simlarly we can prove (ii) is also false..
For case (iii) , we have :
LHS = R1 + R2.R3
= Φ + R2.R3
= R2.R3 [ As R + Φ = R like additive identity ]
RHS = (R1 + R2) . (R1 + R3)
= ( Φ + R2) . ( Φ + R3)
= R2.R3 [ As R + Φ = R like additive identity ]
Hence only (iii) is true
So none of the options of the given question is true..