Sets and Relations

Sets A, B have m, n elements, with A’s subset count 56 more than B’s. Find m and n via prime factorisation of 2^m−2^n=56, then the distance from P(m,n) to Q(−2,−3).

Set A is an open square defined by |a−5|<1 and |b−5|<1; set B is a filled ellipse. Determine whether A⊂B, B⊂A, or neither, by checking the square's corners against the ellipse.

A has 2 elements, B has 4 elements. Find the number of subsets of A×B having 3 or more elements, using the complement of small subset counts.