If A={1,2,3} and B={0,1}, how many functions are there from A to B?

Correct answer: 8

The governing counting principle is that a function from A to B assigns exactly one element of B to each element of A. Set A has three independent inputs: 1, 2, and 3. For each input, there are two possible output choices, 0 or 1, from set B. By the multiplication principle, the total number of assignments is 2 × 2 × 2 = 2^3 = 8, or more generally |B|^|A|. Each different assignment gives a different function, even when some outputs are repeated. Therefore option A, 8, is correct. The values 6, 5, and 3 undercount the possible assignments and do not follow the required power rule. No one-to-one or onto condition is imposed, so all assignments are included.