$g(.)$ is a function from A to B, $f(.)$ is a function from B to C, and their composition defined as $f(g(.))$ is a mapping from A to C.

If $f(.)$ and $f(g(.))$ are onto (surjective) functions, which ONE of the following is TRUE about the function $g(.)$ ?

Let $P$ be the partial order defined on the set {1,2,3,4} as follows:

$P = \{(x, x) \mid x \in \{1,2,3,4\}\} \cup \{(1,2), (3,2), (3,4)\}$

The number of total orders on {1,2,3,4} that contain $P$ is _________.

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$. The number of possible values of $|A|$ is _______

Consider the following sets, where n > 2:
S1: Set of all n x n matrices with entries from the set {a, b, c}

S2: Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0, 1, 2}

Which of the following choice(s) is/are correct?