Final answer:
The claim that prisons and the military would not embrace Theory X is false; both are total institutions where control and discipline align with Theory X principles.
Step-by-step explanation:
The statement that institutions such as prisons and the military are unlikely to embrace Theory X is false. Theory X assumes that employees (or in these cases, inmates or soldiers) are inherently lazy and unproductive, requiring control and the use of punishments to ensure that they follow rules and meet expectations. Both prisons and the military are total institutions where a high level of control is exerted over the individuals within them, and where a structured system of discipline and order is necessary to maintain function and security. Therefore, elements of Theory X are very likely to be found in both types of institutions.