For each of the following conjectures, determine what method of proof or

disproof would be the most efficient or elegant method for proving the statement. You need not write a formal proof $($though you can$)$ but you must answer in a structured paragraph format, detailing your reasoning, mathematical principles used, and any necessary calculations.

a$)$ If x is a positive integer and x$2=$ x$,$ then x $=$x$.$

b$)$ If x is an positive integer and $($x $+1)3=$ x$3+2$x$2+2$x $+1,$ then x$2=$x$.$

c$)$ If n $>=0,$ then log$2$ n $>=$ n

$100$ for all n