Step 1: Understand the function of each gene.
- Gene 'i' encodes Permease, which helps in the transport of substances.
- Gene 'z' encodes the Repressor, which controls gene expression.
- Gene 'y' encodes Transacetylase, involved in acetylation processes.
- Gene 'a' encodes \(\beta\)-Galactosidase, which breaks down lactose.
Step 2: Matching the options.
Thus, the correct matching is:
- (A) 'i' matches with (I) Permease.
- (B) 'z' matches with (II) Repressor.
- (C) 'y' matches with (III) Transacetylase.
- (D) 'a' matches with (IV) \(\beta\)-Galactosidase.
Conclusion:
The correct answer is (3) (A) - (I), (B) - (II), (C) - (III), (D) - (IV).
Final Answer:
\[
\boxed{\text{The correct answer is (A) - (I), (B) - (II), (C) - (III), (D) - (IV).}}
\]