Let M {\displaystyle {}M} and N {\displaystyle {}N} be sets, and let f : M → N {\displaystyle {}f\colon M\rightarrow N} be a mapping. Let ∼ {\displaystyle {}\sim } denote an equivalence relation on N {\displaystyle {}N} . Show that via x ≡ x ′ {\displaystyle {}x\equiv x'} if f ( x ) ∼ f ( x ′ ) {\displaystyle {}f(x)\sim f(x')} holds, an equivalence relation on M {\displaystyle {}M} is defined.
