Let x and y be functions Let x and y be functions, x R y (x...

Question

Question

Let x and y be functions

Let x and y be functions, x R y (x is related to y

engineering Computer-Science

Answer 1

Answer #1

Answer:

O(g(n)) is the set of functions with smaller or same order of growth as g(n).

Eg. O(n^2) includes all functions like O(1), O(n), O(n^2) and O(nlogn).Now coming to your question.

Let x, y, z be three growth rate functions.

And lets assume xRy & yRz....if with these 2 assumptions we can conclude xRz, then R is transitive...

xRy: x is same order or smaller order than y.
yRz: y is same order or smaller order than z.

Thus xRz, proved.

xRz: x is same order or smaller order than z.

For eg. You can take
x=O(1)
y=O(n)
z=O(n^2)

Answer 2

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