Final answer:
The statement is false as there are media that are both selective and differential, such as MacConkey agar which selects for gram-negative bacteria and differentiates lactose fermenters.
Step-by-step explanation:
The statement that a given medium can be either selective or differential but not both is false. Selective media are designed to favor the growth of particular microorganisms and inhibit the growth of others by including substances like antibiotics or specific growth conditions. Differential media contain compounds that allow us to distinguish between different types of bacteria based on their growth patterns, such as changes in colony color or medium due to metabolic byproducts. Some media are both selective and differential, assisting in the identification of bacteria by biochemical methods. An example is MacConkey agar, which is both a selective medium for gram-negative bacteria and differential by indicating lactose fermentation.