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In the case of the tryptophan operon, the co-repressor tryptophan, when complexed to the repressor is able to bind to the operator site and stop the rna polymerase from transcribing the tryptophan biosynthesis genes. however, with the lactose operon, the repressor when complexed to the inducer lactose is not able to bind to the operator site which then allows the rna polymerase to transcribe the lactose metabolism genes.

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Final answer:

The statement is true; the tryptophan operon is repressed by the tryptophan-activated repressor while the lactose operon is induced by the presence of lactose, which prevents the repressor from binding.

Step-by-step explanation:

The statement given is true. In the case of the tryptophan operon, the co-repressor tryptophan, when complexed with the repressor, is indeed able to bind to the operator site and inhibit RNA polymerase from transcribing the tryptophan biosynthesis genes. This is an example of a repressible system where the presence of tryptophan activates the repressor and shuts down the operon.

Conversely, in the case of the lactose operon, which is an inducible system, the presence of the inducer lactose prevents the repressor from binding to the operator site. This allows RNA polymerase to bind to the promoter and initiate transcription of the lactose metabolism genes, enabling the digestion of lactose when it is present in the environment.

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