Question $1$:

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.

$1.$ The state of a chess board can be represented by a two$-$dimensional array.

$2.$ The state of a sliding$-$tile puzzle can be represented by a two$-$dimensional array.

$3.$ Sorting the numbers in a list in increasing order helps later in efficiently finding if the given number is in that list or not.

$4.$ The first element of a list is its head and the last element of a list is its tail.

$5.$ The head of a stack is its top and the tail of a stack is its bottom.

$6.$ Removing the element at the top of a stack is called "pushing".

$7.$ A queue is a FILO $($first$-$in$-$last$-$out$)$ structure.

$8.$ A stack is a FIFO $($first$-$in$-$first$-$out$)$ structure.

$9.$ All nodes at the same depth in a tree have the same ancestors.

$10.$ All nodes at the same depth in a tree have the same descendants.