Let $F$ be the set of all functions from $\{1, \ldots, n\}$ to $\{0,1\}$. Define the binary relation $\preccurlyeq$ on $F$ as follows:
$\forall f . g \in F, f \preccurlyeq g$ if and only if $\forall x \in\{1, \ldots, n\}, f(x) \leq g(x)$, where $0=1$.
Which of the following statement(s) is/are TRUE? re TRUE?
$A=\{0,1,2,3, \ldots\}$ is the set of non-negative integers. Let $F$ be the set of functions from $A$ to itself. For any two functions, $f_1, f_2 \in \mathrm{~F}$ we define
$$\left(f_1 \odot f_2\right)(n)=f_1(n)+f_2(n)$$
for every number $n$ in $A$. Which of the following is/are CORRECT about the mathematical structure $(\mathrm{F}, \odot)$ ?
Let Zn be the group of integers {0, 1, 2, ..., n − 1} with addition modulo n as the group operation. The number of elements in the group Z2 × Z3 × Z4 that are their own inverses is __________.