It is not necessary that for a deadlock to happen , mutual exclusion must be there..It may happen that a solution can suffer from mutual exclusion as well as deadlock.
Consider the following code-snippet as a counter example :
Let we have P[0] , P[1] .. , P[4] be the processes and M[0] ,......M[4] be the mutex locks(binary semaphore) initialised to 1 and process P[i] executes :
wait(m[i]) ;
wait(m[(i+1) mod 4];
critical section
signal(m[i]) ;
signal(m[(i+1) mod 4];
Here say P[0] and P[1] can enter simultaneously thereby violating mutual exclusion property.
For deadlock to happen , for each P[i] we pre empt them after executing the first statement only.So we will have circular wait condition when each of these come to execute the second wait() statement and no P[i] can enter into critical section thereby causing deadlock.
Hence the given assertion should be false.