Final answer:
The assertion that the action potential would reach +60mV if K+ channels did not open is false, as action potentials typically peak around +30mV to +40mV due to the inactivation of Na+ channels. Na+ does continue to enter the cell until reaching its Nernst equilibrium, but this is normally curtailed by Na+ channel inactivation.
Step-by-step explanation:
The statement that the height of the action potential would increase to +60mV if the K+ voltage-gated channels did not open at all is FALSE. This is because, during an action potential, it is the influx of Na+ that initially depolarizes the membrane, increasing the internal voltage of the cell. Normally, the membrane potential reaches about +30mV to +40mV, not +60mV. The K+ channels opening are responsible for repolarizing the membrane, meaning that they help the cell to return to its resting membrane potential. If the K+ channels didn't open, the cell would not be able to repolarize as efficiently, but the height of the action potential would not necessarily reach higher than normal because the voltage-gated Na+ channels would eventually become inactivated, stopping further Na+ entry.
The second part of the statement suggests that Na+ would continue to enter the cell until it reached its Nernst equilibrium, which is TRUE, although the Na+ channels will inactivate, preventing a continuous influx. Normally, the action potential peaks due to the inactivation of Na+ channels and the delayed opening of K+ channels that facilitate repolarization. Therefore, while the ongoing entry of Na+ contributes to depolarization, it is curtailed by channel inactivation, and the K+ channels are essential for repolarization.