Prove That A’∪B = U ⇒ A ⊂ B
Question:
For any two sets \( A \) and \( B \), prove that:
\[ A’\cup B=U \Rightarrow A\subset B \]Solution
\[ A’\cup B=U \]Taking complement on both sides,
\[ (A’\cup B)’=U’ \] \[ A”\cap B’=\phi \] \[ A\cap B’=\phi \] \[ A\subset B \]Hence proved.