Suppose jim isolated four e. coli mutants, mut1 to mut4, that showed abnormal expression of the lac permease protein. to identify the defect in each mutant, he determined the relative levels of lac permease protein in each mutant. he also generated f\' plasmids that contained the wild type (wt) lac operon or the lac operon from each of the four mutants. he determined lac permease protein levels in partial diploids of wild type cells containing f\' lac from each mutant and mutant cells containing wild type f\' lac. all measurements were carried out in cultures grown in the presence ( ) or the absence (–) of lactose and glucose, as shown in the table in cell genotype / f\' plasmid genotype format.

I found the full exercise on the internet and attached is table with the results. 

The task is: "Identify the defect in each mutant."

For mutant 1, the defect is a deletion of the repressor gene. The wt cell contains all the genes that are important to test the questions for the lac permease protein (that's why it is used in the experiment). With the wt cells the table shows that there was only, and always, lac permease production when lactose was present. The fact that, when considering the mut1 cells or the wt cells with the mut1 lac operon plasmid (F' lac from wt/mut1), there was always lac permease production regardless of the presence or absence of lactose, and in the F' lac from mut1/wt cells there wasn't, tells us that there is a deletion of the repressor gene operator in the mut1 cells. That repressor binds to the operator when lactose is absent. This is a gene that is outside the operon and therefore there is no repression when considering mut1 cells.

For mutant 2, the defect is a deletion of the operator. There is always production of lac permease protein, even when there isn't lactose, which means that there isn't an operator for the repressor to bind to. The operator is part of the operon lac and therefore, if it is not present in mut2's operon lac, there won't ever be repression of this operon.

For mutant 3, the defect is a defective promotor. Because there seems to be no problem with the regulation of the operon lac when lactose is absent, and there isn't any production of lac permease even when lactose is present, the problem is the activation of the operon by the promotor. When the promotor wt is present there is no problem and the lac permease production occurs normally.

For mutant 4, the defect is a defective CAP-binding site. When there is a defective CAP-binding site, the CAP protein cannot bind to the operon. The CAP protein binds to the lac operon whenever glucose is low so that the lac operon is activated. When considering only mut4 cells this activation is not present which indicates a problem with this activation process. If there is normal production of lac permease whenever wt lac operon is present, it means that the problem is on the actual binding site of the mut4 operon and not in the CAP protein.