Self doubt on Asymptotic Notations closed

Question

The iterated logarithmic function is defined as:

$logn=0;$ $if$ $n\leq1$   $(or)$  $logn=1+log(logn);$ $if$ $n>1$

Which of the following is/are $True?$

$(1)logn=O(log(logn))$

$(2)(logn)!=O(logn)$

$(3) logn)^{n}=O((logn)!)$

$A)(1)$ $and$ $(2)$$only$        $B)(1) and  (3) only $           $C)(2)$ $and$ $(3)$ $only $              $D)(1),(2)$ $and$ $(3) $

Comments

https://gateoverflow.in/160273/algo-doubt