MadeEasy Test Series: Digital Logic - Logic Gates

Question

A bulb in a stair case has two switches, one switch being at the ground floor and other at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. What is the minimum number of NAND gates required to implement such system?
 

In explanation, they consider it as XOR gate but as given in the question “The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch” so I think,  it should be OR gate. What should be the answer? OR or XOR

Comments

Yes, i'm also confused . why XOR but not the OR gate.

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https://www.quora.com/A-bulb-has-two-switches-one-on-the-first-floor-and-another-on-the-second-floor-It-can-be-switched-ON-and-OFF-by-any-one-of-the-two-switches-irrespective-of-the-second-switch-What-logic-gate-does-the-logic-of-switching-the-bulb-represents