A power supply with a 24-pin motherboard connector can safely be installed in a motherboard that has a 20-pin connector without the need for an adaptor
This statement is correct. A 24-pin power supply can usually be connected to a 20-pin motherboard connector as the extra four pins are designed to provide additional power for more demanding components and may not be necessary for all motherboards. However, it is essential to align the connector properly to ensure the correct pins are connected, and the power supply can operate safely.