State for each of the following statements whether it is true or false, by entering a T for the statements that are true and an F for the statements that are false. Please mention the statement number before each answer, so that answers can be related to the statements.

$(1)$ If there are m$\text{'}$ students and n$\text{'}$ courses such that different students may be enrolled in different courses, then the enrollment of all students in these courses cannot be represented by a single two$-$dimensional array at all.

$(2)$ If there are p$\text{'}$ courses and q$\text{'}$ instructors such that some courses have multiple sections and different instructors may teach different sections of the same course, then the assignment of all instructors to courses cannot be represented by a single two$-$dimensional array at all.

$(3)$ Sorting the numbers in a list in non$-$increasing order does not help at all later in efficiently finding if the given number is in that list or not.

$(4)$ A binary tree is a tree in which each node except the leaves has exactly two descendants.

$(5)$ Multiple nodes in a tree can have the same number of descendants.

$(6)$ Adding an element at the top of a stack is called $``$popping$\text{'}\text{'}.$

$(7)$ A queue is not a LIFO $($last$-$in$-$first$-$out$)$ structure.

$(8)$ A stack is not a LILO $($last$-$in$-$last$-$out$)$ structure.

$(9)$ It is possible to have an even number of nodes at depths m$\text{'}$ and m$\text{'}+1$ in a tree for one or more values of m$\text{'},$ where m$\text{'}$ is a non$-$negative integer.

$(10)$ It is possible to have a node in a tree such that the number of descendants of this node is greater than the number of its ancestors.