If \( A \) and \( B \) are subsets of the universal set \( U \), then show that (i) \( A \subset...

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If \( A \) and \( B \) are subsets of the universal set \( U \), then show that
(i) \( A \subset A \cup B \)
(ii) \( \mathrm{A} \subset \mathrm{B} \Leftrightarrow \mathrm{A} \cup \mathrm{B}=\mathrm{B} \)
\( \mathrm{P} \)
(iii) \( (\mathrm{A} \cap \mathrm{B}) \subset \subset^{\circ} \)
W)
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