# POTD2 - 9 S ∩ U ∪ T ∩ U = 2 4 6 8 10 ∩ 1 3 5 7 9...

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MATH 135 Fall 2005 Problem of the Day #2 Show the equivalence of (a) NOT ( P AND Q ) with (NOT P ) OR (NOT Q ) (b) NOT ( P OR Q ) with (NOT P ) AND (NOT Q ) (c) P = Q with (NOT Q ) = (NOT P ) Solution to POTD # 1 ( S T ) U = ( { 2 , 4 , 6 , 8 , 10 } ∩ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } ) U = { 2 , 4 , 6 , 8 , 10 } ∪ { 1 , 3 , 5 , 7 , 9 } = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } S ( T U ) = S ( { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } ∪ { 1 , 3 , 5 , 7 , 9 } ) = { 2 , 4 , 6 , 8 , 10 } ∩ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } = { 2 , 4 , 6 , 8 , 10 } ( S T ) U = ( { 2 , 4 , 6 , 8 , 10 } ∪ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } ) U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } ∩ { 1 , 3 , 5 , 7 , 9 } = { 1 , 3 , 5 , 7
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Unformatted text preview: , 9 } ( S ∩ U ) ∪ ( T ∩ U ) = ( { 2 , 4 , 6 , 8 , 10 } ∩ { 1 , 3 , 5 , 7 , 9 } ) ∪ ( { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } ∩ { 1 , 3 , 5 , 7 , 9 } ) = ∅ ∪ { 1 , 3 , 5 , 7 , 9 } = { 1 , 3 , 5 , 7 , 9 }...
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