The Full Form of WLOG is Without loss of generality.

Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used to indicate the assumption that follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general. The other cases are also proven by some symmetry — or another equivalence or similarity. As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases.