
The best way to solve this type of problem is to write out the expected
phenotype for the particular mutation and then match the prediction to
the data. Remember that we are assuming that these are loss of function
mutations (no super repressors, etc.).
a) E1 would give LLLH. Mutation D has this phenotype.
b) E2 would give LLHL. Mutations E and G have this phenotype.
c) P would give LLLL. Mutations A and C have this phenotype.
d) R or O
would give HHHH. Mutations F and B have this phenotype.
This gives the map:

e) Using the gene notation from the diagram:
Strain (1):
Strain (2):
Strain (3): 
Strains (4) and (5) deal with mutations in the operator or repressor. In
this case, it is easier to predict the outcome and match it to the
data:
If in repressor:

This looks like mutant F. Therefore, F is in repressor gene.
If in operator:
. Looks like B.
This gives the map: