#1. Let 𝑓: 𝑋 → 𝑌 be a function on 𝑋 into 𝑌. Define a relation 𝜌 on 𝑋 by 𝑥1𝜌𝑥2, if and only if, 𝑓(𝑥1) = 𝑓(𝑥2). Then 𝜌 is an equivalence relation on 𝑋.
#1. Let 𝑓: 𝑋 → 𝑌 be a function on 𝑋 into 𝑌. Define a relation 𝜌 on 𝑋 by 𝑥1𝜌𝑥2, if and only if, 𝑓(𝑥1) = 𝑓(𝑥2). Then 𝜌 is an equivalence relation on 𝑋.