Operation table/Mappings on set with 2 elements/Exercise

Let ${}M$ be the set of all mappings from the set ${}\{0,1\}$ to itself, that is

${}M={\left\{F:\{0,1\}\rightarrow \{0,1\}\mid F{\text{ mapping}}\right\}}\,.$

Denote the elements of ${}M$ with certain symbols, and establish a value table for the binary operation on ${}M$ given by the composition of mappings.

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