Final answer:
Credit cards with magnetic strips can be damaged by permanent magnets; hence, they are the most susceptible to damage. It's true that such cards should not be placed near permanent magnets.
Step-by-step explanation:
Out of the items listed, credit cards are most susceptible to damage from permanent magnets because credit cards typically have a magnetic strip that contains sensitive data which can be erased or corrupted when exposed to a strong magnetic field. Cellular telephone antennas, polarized power connectors, and AA batteries, on the other hand, do not rely on magnetism for their operation and are relatively unaffected by external magnetic fields.
Answering the true or false question, it is true that it is not recommended to place credit cards with magnetic strips near permanent magnets, as the magnetic field can damage the data encoded on the strips.