A system X is neither in thermal equilibrium with Y, nor with Z. The systems Y and Z -
May be in thermal equilibrium
Let the temperatures of X, Y and Z be Tx, Ty and Tz, respectively.
Now,
Tx ≠ Ty,
and
Tx ≠ Tz.
This does not tell us anything about Ty and Tz, except that they are not equal to Tx.
So, Ty = Tz, and Ty ≠ Tz, both are possibilities!
Hence, option (c) is correct.