Answer
$S$ is not $Proposition$.
Work Step by Step
Let
$p$= "$S$ is true"
$q$= "$U$nicorns live"
Using the above interpretation we can then rewrite S as” $(p \rightarrow q) \rightarrow q$”
Let us first assume that $S$ is true, and then $p$ is true. However we cannot determine that $q$ is true or false, because the statement will be true if $q$ is true ($(p \rightarrow q) \rightarrow q$ is then false) and the statement will also be true if $q$ is false ($(p \rightarrow q) \rightarrow q$ is then true)
Next, let us assume that $S$ is false, then$p \rightarrow q$ is true and $q$ is false. But then we can also know that $p$ is false (since $q$ is false and $p \rightarrow q$ is true). If $p$ is false, then this also states that $S$ is false. Thus we note that this assumption is also correct.
Conclusion: we note that we cannot determine if $S$ is true of if $S$ is false (both options are possible).
By the definition of a proposition, $S$ is then not a proposition.
