Final answer:
A posttest loop does not iterate if the initial Boolean expression is false, as it checks the condition after the loop's body executes.
Step-by-step explanation:
The statement that a posttest loop does not perform any iteration if the Boolean expression is false to begin with is True. A posttest loop, such as the do-while loop in many programming languages, checks the condition after the body of the loop has executed. If the Boolean expression evaluates to false at the beginning, the loop will not execute because the condition is only checked after one iteration has already occurred.