$20)$ Provide True or False for the following statements:

a$.$ Algorithm A and B have a worst$-$case running time of O$($n$)$ and O $($log n$),$ respectively. Therefore, algorithm B always runs faster than algorithm A$.$

b$.$ f$($n$)=$ O$($g$($n$))$ if there exist positive constants n$0$ and c such that f$($n$)<=$ cg$($n$)$ for all n

$>=$ n$0.$

c$.\backslash$Omicron notation denotes the worst$-$case running time complexity with a lower bound.

d$.$ f$($n$)=\backslash$Theta $($g$($n$))$ if there exist positive constants n$0,$ c$1$ and c$2$ such that c$1$g$($n$)<=$ f$($n$)<=$ c$2$g$($n$)$ for all n $>=$ n$0.$

e$.$ If for an algorithm time complexity is given by O$($n$)$ then complexity of it is linear and for O $(1)$ it is said to be constant.