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For all sets A and B, A – (A – B) = A ∩ B

0 2 Views | Posted 4 months ago
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    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    L . H . S . = A − ( A − B ) = A − ( A ∩ B ' )                                                     [ ? A − B = A ∩ B ' ]                               = A ∩ ( A ∩ B ' ) = A ∩ [ A ' ∪ ( B ' ) ' ]                                 [ ? ( A ∩ B ) ' = A ' ∪ B ' ]                               = A ∩ [ A ' ∪ B ]                                                                                                                     [ ? ( A ' ) ' = A ]                               = ( A ∩ A ' ) ∪ ( A ∩ B ) = ? ∪ ( A ∩ B )                                 = A ∩ B = R . H . S . H e n c e ,     t h e     g i v e n     s t a t e m e n t     i s     p r o v e d .

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