I am trying to translate this to Latin:
Today, at the university (I study Computer Science), we were taught about the set theory. The professor was explaining to us why the cardinal number of a union of sets is not always equal to the sum of the cardinal number of sets in that union: "If that were true, a dog should have eight legs. A dog, namely, has two front legs, two hind legs, two left legs and two right legs. The sum of the cardinal numbers of those sets is eight (four times two), but the cardinal number of the union of those sets is, of course, four."
This is my attempt:
Hodie in universitate (ego studeo scientiam computorum) docebamur de theoria unionum. Professor nobis explicabat, cur numerus cardinalis unionis unionum non semper sit summa (additio) cardinalum numerorum unionum: "Si hoc veritas esset, canis debet octo crura habere. Canis enim habet duo crura antica, duo crura posteriora, duo crura laeva, et duo crura dextera. Summa (additio) numerorum cardinalium earum unionum octo (quater bini) est, sed numerus cardinalis unionis earum unionum, sane, quattuor est.".