ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4167 on D77: Set union

Superset of binary union iff superset of both sets in the union

Formulation 0

Let $X, A, B$ each be a D11: Set such that

(i)	$A \cup B$ is the D77: Set union of $A$ and $B$

Then \begin{equation} A \cup B \subseteq X \quad \iff \quad A \subseteq X, \; B \subseteq X \end{equation}

Proofs

Proof 0

Let $X, A, B$ each be a D11: Set such that

(i)	$A \cup B$ is the D77: Set union of $A$ and $B$