Consider two functions with natural arguments and positive real values: f; g : N â R+. Consider the following propositions, where c ranges over positive reals, and n, n0 range over the naturals: P : âc : ân0 : ân : n ⥠n0 ! f(n) ⤠cg(n) (this is the de nition of \f(n) is O(g(n))")
Q : ân0 : âc : ân : n ⥠n0 ! f(n) ⤠cg(n)
R : âc : ân0 : ân : n ⥠n0 ! f(n) â¤cg(n)

Required:
a. Are any two of these propositions equivalent, for arbitrary choices of f and g?
b. Is any of the propositions always true, whatever f and g?
c. Can you nd two functions f and g for which R is true ?

Geneva’s manager would like to see some additional information to make sales decisions. enter a formula in cell j4 using the if function to it whether or not the item beaded earrings should go on sale. it will go on sale if its current sales rank (in cell g4) is 8th or lower. (hint: if the cell value is greater than or equal to 8, it will go on sale.)if this condition is true, the item will go on sale. (hint: the if_true value should be “yes”.)if this condition is false, the item doesn’t need to go on sale. (hint: the if_false value should be “-”.)copy the formula created in cell j4 to the range j5: j14

Selective incapacitation is a strategy to reduce prison population

Linux is distributed under gnu gpl. why is this important? a. it ensures that only torvalds can profit from the sale of linux b. it prevents unknowledgeable users from downloading programs they don't know how to operate. c. it provides protection for the developers who created linux. d. it states that anyone can copy, modify, and share the program if changes are made public.