List of top Mathematics Questions on Functions asked in GATE CS

Let \( \mathcal{F} \) be the set of all functions from \(\{1, \dots, n\}\) to \(\{0,1\}\). Define the binary relation \(\preceq\) on \( \mathcal{F} \) as follows: \[ \forall f, g \in \mathcal{F}, \quad f \preceq g { if and only if } \forall x \in \{1, \dots, n\}, \quad f(x) \leq g(x), \quad {where } 0 \leq 1. \] Which of the following statement(s) is/are TRUE?
g(periodcentered) is a function from A to B, f(periodcentered) is a function from B to C, and their composition defined as f(g(periodcentered)) is a mapping from A to C. If f(periodcentered) and f(g(periodcentered)) are onto (surjective) functions, which ONE of the following is TRUE about the function g(periodcentered)?