Solution 5 :
We observe that , all the three functions are compressed / expanded versions of each other .
Thus, if we can prove any one of the given statements to be true/false , the other ones become explicitly implied (in case of continuous signals) .
(1)
From the given
information , we have
 Let
T be the period of x(t) . Then , we have
Inputting x(t + T) in the LSI system, will
give the output as follows :
Thus we have
which proves the first statement to be true. And the
period of the resultant signal is also compressed by half.
NOTE : The given system is linear and shift variant
.
Thus the remaining three statements are also true .
And the period of the expanded signal will be twice that of original signal.
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