This is just an assumption, but the bit-wise AND / OR / NOT option was probably chosen (in the days of 8-bit BASIC implementations) to simplify the implementation and flexibility compared to zero vs non-zero logic.
You could not make the language too complicated, as it was during the days of the “home computer”, when the processor cycles were in kilohertz, and the memory was in kilobytes, and storage devices where it was rarely or expensive or primitive (for example, a device for recording on paper tape or hastily adapted tape cassette player / player).
Dartmouth BASIC (the beginning of everything, since 1964, http://bitsavers.trailing-edge.com/pdf/dartmouth/BASIC_4th_Edition_Jan68.pdf ), there wasn’t even AND / OR / NOT, not even as keywords for IF.
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