How can I explain the intuition behind the First Isomorphism Theorem for modules or for rings to a lay person in mathematics, like to a non-scientist. I want to use a very elementary example in life.
Statement of the First Isomorphism Theorem: Let $R$ and $S$ be rings and $f:R\to S$ be a ring homomorphism. Then $R/\ker(f)\cong f(R)$, where $\ker(f)$ is the kernnel of $f$.