pts $(2$ pts each$)$Mark the following statements as TRUE or FALSE by circling the correct answer. No need to provide any justification.$[$TRUE$/$FALSE $|$Problem Statement: If an algorithm A has worst$-$case time complexity O$($f$($n$)),$ then there exists a positive constant c such that the maximum number of operations that the algorithm A executes on any input of size n is less than or equal to c $($n$).[$ TRUE$/$FALSE$]0($n$2).$The worst$-$case runtime complexities of Bubble sort, Insertion sort, and Merge sort are all$[$TRUE$/$FALSE $]$Consider the following list, where each $($name$,$ height$)$ pair represents a student in a class:$($Amy$,150$cm$),($Bianca$,160$cm$),($Connor$,170$cm$),($Diego$,165$cm$),($Emma$,160$cm$)$Suppose we run a sorting algorithm A to sort the students in this list in increasing order of height, and the algorithm returns the following ordering of the students:$($Amy$,150$cm$),($Emma$,160$cm$),($Bianca$,160$cm$),($Diego$,165$cm$),($Connor$,170$cm$)$True or False: This is sufficient to prove that the sorting algorithm is not stable.$[$TRUE$/$FALSE$]$Suppose algorithm A has a runtime of $($n log n$),$ and algorithm B has a runtime of O$($n$?).$ Then there must exist a non$-$negative integer n where algorithm A runs faster than algorithm B for all inputs of size n$.[$ TRUE$/$FALSE $]$If f$($n$)=2$log $(3$n$/8)?,$ then Mn$)=$ O$($n$\text{'}*)($all log$\text{'}$s are base$-2).$I TRUE$/$FALSE $]$If f$($n$)$ and g$($n$)$ are the worst$-$case and best$-$case runtimes, respectively, of an algorithm A$,$then we must have f$($n$)=2($g$($n$)).[$TRUE$/$FALSE $]$There does not exist a function f: R R such that f$($x$)=$ S$2(2$x$3)$ and x$)=0($x$2).$