Problem 7 [10 pts] Prove that

[([n],[3])]^(2)

is

\\\\Theta (n^(6))

. Use the basic definitions, i.e., find a constant

M

and a\ multiplicative constant

C

and then apply the definition of

O(n^(6))

to prove that

[([n],[3])]^(2)

is

\\\\Theta (n^(6))

. Then find\ another constant

M^(')

and another multiplicative constant

C^(')

and then apply the definition of

\\\\Omega (n^(6))

to prove\ that

[([n],[3])]^(2)

is

\\\\Omega (n^(6))

.

Problem 7 [10 pts] Prove that [(n3)]2 is (n6). Use the basic definitions, i.e., find a constant M and a multiplicative constant C and then apply the definition of O(n6) to prove that [(n3)]2 is (n6). Then find another constant M and another multiplicative constant C and then apply the definition of (n6) to prove that [(n3)]2 is (n6)