Investigating the validity of an argument "If Mike performs well in her examination, he will get a scholarship, if Mike gets a scholarship, he will travel abroad. Mike got a scholarship therefore she performed well in her examination".
 A: A valid argument is one in which for every case where the antecedent is true; the consequent must not be false. 

"If Mike performs well in her examination, he will get a scholarship,
  if Mike gets a scholarship, he will travel abroad. Mike got a
  scholarship therefore she performed well in her examination".

I have read your expressions as:
$W\rightarrow S\tag{1}\label{1}$
$S\rightarrow T\tag{2}\label{2}$
$S\tag{3}\label{3}$
$((W\rightarrow S)\land S)\rightarrow W\tag{4}\label{4}$
,where W, S and T represent "Mike did well", "Mike got a scholarship", and "Mike Traveled" consecutively. 
($\ref{4}$) is an example of affirming the consequence. It is a common formal fallacy and is not a valid argument. This is because the consequent may be false even when the antecedent is true. (https://en.wikipedia.org/wiki/Affirming_the_consequent)
An example of a valid argument that can be formed using ($\ref{1}$), ($\ref{2}$), and ($\ref{3}$) is ($\ref{5}$):
$((S\rightarrow T)\land S)\rightarrow T\tag{5}\label{5}$
($\ref{5}$) takes the form of a valid argument because there is no way for the consequent to be false when the antecedent is true. This can be checked by a truth table. (https://en.wikipedia.org/wiki/Modus_ponens)
