As a genetics historian, you are repeating some of the classic experiments conducted by Jacob and Monod with the lactose operon in E. coli. You use an F plasmid to construct several E. coli strains that are partially diploid for the lac operon. You construct strains with the following genotypes: 

(1) I⁺OcZ⁺Y^-/I⁺O⁺Z⁻Y⁺, 

(2) I⁺OcZ^-Y⁺/I⁺O⁺Z⁺Y⁻, 

(3) I^-O⁺Z⁺Y⁺/I⁺O⁺Z⁻Y⁻, 

(4) I^sO⁺Z^-Y⁻/I⁺O⁺Z⁺Y⁺, and 

(5) I⁺O^cZ⁺Y⁺/I^sO⁺Z−Y⁺. 

(a) Which of these strains will produce functional β-galactosidase in both the presence and absence of lactose? 

(b) Which of these strains will exhibit constitutive synthesis of functional β-galactoside permease? 

(c) Which of these strains will express both gene Z and gene Y constitutively and will produce functional products (β-galactosidase and β-galactoside permease) of both genes? 

(d) Which of these strains will show cis dominance of lac operon regulatory elements? 

(e) Which of these strains will exhibit trans dominance of lac operon regulatory elements?