Is the relation < a strict total order?

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I really stuck with a question in the class exercise:

Consider the set $X=2^Y$ where $Y=\{1,2,3,4,5,6,7,8,9\}$ and the order on X defined by $x < y$ if and only if $x \subset y$, that is if $x$ is a subset of $y$. Is the relation < $x$ strict total order?

Please elaborate a bit on the question. Just started my intro to abstract algebra.

I feel this is not strict total order. But, couldn't find an counter example to it.