Its the question from NCERT textbook Ch - 1(Pg - 26) Miscellaneous Exercise - Q.2 (iv)

The statement given in the question may or may NOT be true.

In the example of sets which you have taken, the given statement is true.

 

However, look at the following example:

Let A = {1, 2}, B = {0, 6, 8} and C = {0, 1, 2, 6, 9}

 

Here, A is not a subset of B and B is not a subset of C. But, A is a subset of C.