Problem 1 (20 points) Are the following statements true or false? For each part, first state whether it is true or

false, then prove your claim.

1.1 () = ( (^2))

1.2 log( ()) = (log(())) () = (())

1.3 () + () = ( ( ()+()) /

2 )

1.4 log(!) = ( log())

Problem 1 ( 20 points) Are the following statements true or false? For each part, first state whether it is true or false, then prove your claim. 1.1f(n)=O(f(n2)) 1.2log(f(n))=(log(g(n)))f(n)=O(g(n)) 1.3f(n)+g(n)=(2f(n)+g(n)) 1.4log(n!)=(nlog(n))