Final answer:
The statement about bi-directional relationships between entities is false; they do not always operate in both directions. However, in physics, Newton's third law exemplifies a symmetrical force relationship, and a unit analysis of E=mc² using F=ma and E=Fd is indeed possible and shows consistency in units.
Step-by-step explanation:
True or false: Relationships between entities always operate in both directions. This statement is false. The relationship between X and Y in the statement "if X, then Y" is not always symmetrical. For example, Y is necessary for X, but X may not be necessary for Y. This means that while X can lead to Y, the presence of Y doesn't always mean that X has occurred. However, X is always sufficient for the occurrence of Y. This can be applied to physics, where Newton's third law states that for every action, there is an equal and opposite reaction, which illustrates that the forces between two objects are symmetrical.
In the context of verifying the units in the equation E0 = mc², it is true that the relationships F = ma (force equals mass times acceleration) and E = Fd (energy equals force times distance) can show that both sides of the equation have the same units. Here, the relationship operates in a way that the units of force, mass, acceleration, and distance align to confirm the units of energy in terms of mass and the speed of light squared.