Final answer:
A lysogenic cell contains viral DNA as a prophage integrated into the host chromosome, confirming that the statement is true. The prophage is inherited by daughter cells and can affect the host's phenotype. Environmental factors can induce the prophage to switch to the lytic cycle.
Step-by-step explanation:
In the lysogenic cycle, which is one of the two life cycles of a bacteriophage (the other being the lytic cycle), the phage DNA integrates into the bacterial host's genome and becomes a prophage. This prophage is then passed on to subsequent generations of cells as the bacterium replicates its chromosome, potentially changing the phenotype of the bacterial host through a process known as lysogenic conversion or phage conversion. However, environmental stressors like starvation or exposure to toxic chemicals can induce the prophage to excise from the host genome and enter the lytic cycle, leading to the production of new phages and the eventual lysis of the host cell.