Original expression : NOT (a OR b) Disjunctive normal form : NOT a AND NOT b Term : NOT a AND NOT b Positives: ( ) Negatives: ( a b ) Evaluate : true -------------------------------------------------------------------------------------- Original expression : NOT (a AND b) Disjunctive normal form : NOT a OR NOT b Term : NOT a Positives: ( ) Negatives: ( a ) Term : NOT b Positives: ( ) Negatives: ( b ) Evaluate : true -------------------------------------------------------------------------------------- Original expression : a AND (b OR c) Disjunctive normal form : a AND b OR a AND c Term : a AND b Positives: ( a b ) Negatives: ( ) Term : a AND c Positives: ( a c ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND NOT c Disjunctive normal form : a AND NOT c OR b AND NOT c Term : a AND NOT c Positives: ( a ) Negatives: ( c ) Term : b AND NOT c Positives: ( b ) Negatives: ( c ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : NOT (NOT (a AND m)) Disjunctive normal form : a AND m Term : a AND m Positives: ( a m ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : a AND b AND (c OR d) Disjunctive normal form : a AND b AND c OR a AND b AND d Term : a AND b AND c Positives: ( a b c ) Negatives: ( ) Term : a AND b AND d Positives: ( a b d ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND c AND d Disjunctive normal form : a AND c AND d OR b AND c AND d Term : a AND c AND d Positives: ( a c d ) Negatives: ( ) Term : b AND c AND d Positives: ( b c d ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND (c OR d) Disjunctive normal form : a AND c OR a AND d OR b AND c OR b AND d Term : a AND c Positives: ( a c ) Negatives: ( ) Term : a AND d Positives: ( a d ) Negatives: ( ) Term : b AND c Positives: ( b c ) Negatives: ( ) Term : b AND d Positives: ( b d ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND (c AND d) Disjunctive normal form : a AND c AND d OR b AND c AND d Term : a AND c AND d Positives: ( a c d ) Negatives: ( ) Term : b AND c AND d Positives: ( b c d ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND NOT (c AND d) Disjunctive normal form : a AND NOT c OR a AND NOT d OR b AND NOT c OR b AND NOT d Term : a AND NOT c Positives: ( a ) Negatives: ( c ) Term : a AND NOT d Positives: ( a ) Negatives: ( d ) Term : b AND NOT c Positives: ( b ) Negatives: ( c ) Term : b AND NOT d Positives: ( b ) Negatives: ( d ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND (c OR d) AND (e OR f) Disjunctive normal form : a AND c AND e OR a AND c AND f OR a AND d AND e OR a AND d AND f OR b AND c AND e OR b AND c AND f OR b AND d AND e OR b AND d AND f Term : a AND c AND e Positives: ( a c e ) Negatives: ( ) Term : a AND c AND f Positives: ( a c f ) Negatives: ( ) Term : a AND d AND e Positives: ( a d e ) Negatives: ( ) Term : a AND d AND f Positives: ( a d f ) Negatives: ( ) Term : b AND c AND e Positives: ( b c e ) Negatives: ( ) Term : b AND c AND f Positives: ( b c f ) Negatives: ( ) Term : b AND d AND e Positives: ( b d e ) Negatives: ( ) Term : b AND d AND f Positives: ( b d f ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : (a OR b) AND (c OR d) AND (e OR f) AND (g OR h) Disjunctive normal form : a AND c AND e AND g OR a AND c AND e AND h OR a AND c AND f AND g OR a AND c AND f AND h OR a AND d AND e AND g OR a AND d AND e AND h OR a AND d AND f AND g OR a AND d AND f AND h OR b AND c AND e AND g OR b AND c AND e AND h OR b AND c AND f AND g OR b AND c AND f AND h OR b AND d AND e AND g OR b AND d AND e AND h OR b AND d AND f AND g OR b AND d AND f AND h Term : a AND c AND e AND g Positives: ( a c e g ) Negatives: ( ) Term : a AND c AND e AND h Positives: ( a c e h ) Negatives: ( ) Term : a AND c AND f AND g Positives: ( a c f g ) Negatives: ( ) Term : a AND c AND f AND h Positives: ( a c f h ) Negatives: ( ) Term : a AND d AND e AND g Positives: ( a d e g ) Negatives: ( ) Term : a AND d AND e AND h Positives: ( a d e h ) Negatives: ( ) Term : a AND d AND f AND g Positives: ( a d f g ) Negatives: ( ) Term : a AND d AND f AND h Positives: ( a d f h ) Negatives: ( ) Term : b AND c AND e AND g Positives: ( b c e g ) Negatives: ( ) Term : b AND c AND e AND h Positives: ( b c e h ) Negatives: ( ) Term : b AND c AND f AND g Positives: ( b c f g ) Negatives: ( ) Term : b AND c AND f AND h Positives: ( b c f h ) Negatives: ( ) Term : b AND d AND e AND g Positives: ( b d e g ) Negatives: ( ) Term : b AND d AND e AND h Positives: ( b d e h ) Negatives: ( ) Term : b AND d AND f AND g Positives: ( b d f g ) Negatives: ( ) Term : b AND d AND f AND h Positives: ( b d f h ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : a OR b AND (c OR d AND (e OR f AND g AND (h OR i))) Disjunctive normal form : a OR b AND c OR b AND d AND e OR b AND d AND f AND g AND h OR b AND d AND f AND g AND i Term : a Positives: ( a ) Negatives: ( ) Term : b AND c Positives: ( b c ) Negatives: ( ) Term : b AND d AND e Positives: ( b d e ) Negatives: ( ) Term : b AND d AND f AND g AND h Positives: ( b d f g h ) Negatives: ( ) Term : b AND d AND f AND g AND i Positives: ( b d f g i ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : a AND (b OR c AND (d OR (e AND (f OR g OR (h AND i))))) Disjunctive normal form : a AND b OR a AND c AND d OR a AND c AND e AND f OR a AND c AND e AND g OR a AND c AND e AND h AND i Term : a AND b Positives: ( a b ) Negatives: ( ) Term : a AND c AND d Positives: ( a c d ) Negatives: ( ) Term : a AND c AND e AND f Positives: ( a c e f ) Negatives: ( ) Term : a AND c AND e AND g Positives: ( a c e g ) Negatives: ( ) Term : a AND c AND e AND h AND i Positives: ( a c e h i ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : NOT (a OR b) AND NOT (c OR d) AND (e OR f) AND NOT (g OR h) Disjunctive normal form : NOT a AND NOT b AND NOT c AND NOT d AND e AND NOT g AND NOT h OR NOT a AND NOT b AND NOT c AND NOT d AND f AND NOT g AND NOT h Term : NOT a AND NOT b AND NOT c AND NOT d AND e AND NOT g AND NOT h Positives: ( e ) Negatives: ( a b c d g h ) Term : NOT a AND NOT b AND NOT c AND NOT d AND f AND NOT g AND NOT h Positives: ( f ) Negatives: ( a b c d g h ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : a AND (b OR c AND (d OR (e AND (f OR g OR (h AND i) OR j)))) Disjunctive normal form : a AND b OR a AND c AND d OR a AND c AND e AND f OR a AND c AND e AND g OR a AND c AND e AND j OR a AND c AND e AND h AND i Term : a AND b Positives: ( a b ) Negatives: ( ) Term : a AND c AND d Positives: ( a c d ) Negatives: ( ) Term : a AND c AND e AND f Positives: ( a c e f ) Negatives: ( ) Term : a AND c AND e AND g Positives: ( a c e g ) Negatives: ( ) Term : a AND c AND e AND j Positives: ( a c e j ) Negatives: ( ) Term : a AND c AND e AND h AND i Positives: ( a c e h i ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : a AND (b OR c AND (d OR (e AND (f OR g OR (h AND i)) OR j))) Disjunctive normal form : a AND b OR a AND c AND d OR a AND c AND j OR a AND c AND e AND f OR a AND c AND e AND g OR a AND c AND e AND h AND i Term : a AND b Positives: ( a b ) Negatives: ( ) Term : a AND c AND d Positives: ( a c d ) Negatives: ( ) Term : a AND c AND j Positives: ( a c j ) Negatives: ( ) Term : a AND c AND e AND f Positives: ( a c e f ) Negatives: ( ) Term : a AND c AND e AND g Positives: ( a c e g ) Negatives: ( ) Term : a AND c AND e AND h AND i Positives: ( a c e h i ) Negatives: ( ) Evaluate : false -------------------------------------------------------------------------------------- Original expression : NOT (a OR b) AND NOT (c OR d) AND NOT (e OR f) AND NOT (g OR h) Disjunctive normal form : NOT a AND NOT b AND NOT c AND NOT d AND NOT e AND NOT f AND NOT g AND NOT h Term : NOT a AND NOT b AND NOT c AND NOT d AND NOT e AND NOT f AND NOT g AND NOT h Positives: ( ) Negatives: ( a b c d e f g h ) Evaluate : true --------------------------------------------------------------------------------------