Final answer:
A ring of four carbon molecules cannot have double bonds due to the high ring strain.
Step-by-step explanation:
The reason why a ring of four carbon molecules cannot have double bonds is due to the ring strain that would be present. In larger rings, such as cyclohexane, the ring can undergo a puckering to minimize the angle strain. However, in a four-membered ring, the ring strain is too high to accommodate the presence of double bonds.