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Superset**

A 'superset' of a set \(X\) is a set \(S\) which contains all elements of \(X\). We denote this relation by \(S\supseteq X\); \(S\supseteq X\Leftrightarrow\forall a:a\in X\Rightarrow a\in S\). If \(S\neq X\), then we call \(S\) a 'proper' superset of \(X\).