a) Since \$$m \rightarrow n \$$ implies that m divides n, then the product \$$x \times y \$$ should contain one morphism \$$x \times y \rightarrow x \$$ and one \$$x \times y \rightarrow y \$$. So basically, we want \$$x \times y \$$ such as it divides both \$$x \$$ and \$$y \$$. And that's the greatest common divisor of those two numbers: 3

b) Similarly, we want the product to be both a subset of \$$\{a,b,c\} \$$ and \$$\{b,c,d\} \$$. And that is the intersection: \$$\{b, c\} \$$

c) In this one we have that \$$a \times b \rightarrow a \$$ and \\( a \times b \rightarrow b ||) should be a tautology. So this should be the and operator and the value is False

In any case, we can test (not prove) all of those with this Haskell code:

https://gist.github.com/folivetti/e0ded9e8469388b6d00676d394a92c0d