Mapping/Mother of/Aspects/Exercise

1. Let ${}H$ be the set of all (alive or dead) people. Study the mapping

   $\varphi \colon H\longrightarrow H$

   that assigns to every person the mother, with respect to injectivity and surjectivity.

2. What is the meaning of the composition ${}\varphi ^{3}$?
3. How does it look when we take the same mapping but, in the domain, restricted to the set ${}E$ of all only children, and, in the codomain, restricted to the set ${}M$ of all mothers?
4. Be a bit hairsplitting and argue (referring to evolution or religion) that the mapping in (1) is not well-defined.

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