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Consider the cartesian product ab where ab are finite

Question: 1. Consider the Cartesian product A×B, where A,B are finite nonempty sets, each with cardinality greater than 1. There are two functions with domain A×B, called projections, with mapping rules p₁(a, b) = a and p₂(a, b) = b. What is the target space of p₁? Of p₂? Are either of p₁, p₂ one-to-one? Onto?

2. Let A = {0,1,2,3,4}×{0,1,2}, let B = {n | n is a positive factor of 144}, and let f : A → B with f(a₁, a₂) = 2a₁ · 3a₂ . Is f one-to-one? Onto?

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