By using the set algebra , prove that , for any sets A and B A u ( A' n B ) = A u B Deduce , or using set algebra , show that A u ( A' n B ) u [A' n (A u B') n {B u (B' n C}] = A u B u C
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The question test the distributive laws. A u ( A' n B ) = A u B from L.H.S : A u ( A' n B ) = ( A U A' ) n ( A u B ) = S n ( A u B ) = A u B ( proven ) You should be able to solve the second part using the law or the procedure listed above Originally Posted by mathaddict By using the set algebra , prove that , for any sets A and B A u ( A' n B ) = A u B Deduce , or using set algebra , show that A u ( A' n B ) u [A' n (A u B') n {B u (B' n C}] = A u B u C
Originally Posted by mathaddict Deduce , or using set algebra , show that A u ( A' n B ) u [A' n (A u B') n {B u (B' n C}] = A u B u C I tried this one but i couldn't get the prove . Can someone pls spot my mistake . My working : (A u B) u (A' n B' ) n ( B u C ) = S n (B u C ) = B u C wondering , where is the A .
Hello mathaddict Originally Posted by mathaddict I tried this one but i couldn't get the prove . Can someone pls spot my mistake . My working : (A u B) u (A' n B' ) n ( B u C ) = S n (B u C ) = B u C wondering , where is the A . Here's a proof - there might be a quicker one: , using the first result twice , Distributive Law , Complement Law , Identity Law , De Morgan's Law , Distributive Law , Complement Law , Identity Law, Associative Law , Idempotent Law Grandad
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