Answer: Option D
:
D
From (I), if Tauqir is U, then Vusi is V. However we cannot conclude that if Vusi is V, then Tauqir is U.
Let us assume that Tauqir is U. Then, Vusi is V.
from (III), as Vusi is not W, Wasim is V. But both Vusi and Wasim cannot be V.
So, our assumption (that Tauqir is U) itself is not valid.
$\therefore$ Tauqir is not U.
If Tauqir is V, then Shoaib is T [from IV]. In such a case, Usman is V [from II]. Once again it is not acceptable, as Tauqir and Usman both cannot be V.
$\therefore$ the assumption made (that Tauqir is V) is invalid.
$\therefore$ Tauqir is not V.
If Tauqir is S, then Shoaib is T [from IV]. In this case, Usman is V [from II]. As Usman is not W, Tauqir is not S [from V]. This contradicts the assumption that Tauqir is S. So, this is also invalid.
$\therefore$ Tauqir is not S.
As Tauqir is neither V nor S, it is clear from (IV) that Shoaib is not T.
If Vusi is V, then Vusi is not W and thus Wasim is V [From (III)] . This is not possible, as both Vusi and Wasim cannot be V.
$\therefore$ Vusi is not V.
Tauqir can only be either T or W. Now if Tauqir is T, Vusi is U and Wasim is not V [from VI].
But if Vusi is U, then Vusi is not W and thus Wasim must be V, according to (III).
$\therefore$ Tauqir is not T.
Let us summarize the findings till now.
Shoaib: Not T
Tauqir: Not U, Not S, Not V and Not T
Vusi: Not V
So, the only possibility is that Tauqir is W.
From (VI), Vusi is U and Wasim is not V, if and only if Tauqir is T. Now, as Tauqir is not T, it follows that Vusi is not U. It also follows that Wasim is V.
If Shoaib is U, then Usman is W [from VII]. But we know that Tauqir is W, so Usman is not W.
$\therefore$  It follows that Shoaib is not U.
$\therefore$ Shoaib is not U, Shoaib is not T, Shoaib is not W (as Tauqir is W) and Shoaib is not V (as Wasim is V).
$\therefore$ Shoaib is S.
Also, Vusi is neither S nor V or W. Also, Vusi is not U.
$\therefore$ Vusi is T. Thus, Usman has to be U.
So Shoaib, Tauqir, Usman, Vusi and Wasim operate under the names of S, W, U, T and V respectively.