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Published byJeremy Rowles Modified over 3 years ago

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2 x Rxk no-one respects Kay x Rxk everyone respects Kay x Rjx Jay respects someone x Rjx Jay respects everyone x Rjx Jay respects no one x Rxk some one respects Kay

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3 x y Ryx there is someone whom no-one respects x y Rxy there is someone who respects no-one x y Ryx there is someone whom everyone R’s x y Rxy everyone respects someone (or other) x y Ryx no-one is respected by everyone x y Rxy no-one respects everyone x y Rxy someone respects someone x y Rxy everyone respects everyone

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5 ( Sx Rxk ) xx IF x is a student, THEN x respects Kay no matter who x is IF you are a student, THEN you respect Kay no matter who you are every student respects Kay

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6 ( Sx & Rxj ) xx x is a S and x R's j there is no x : who is a S and who R's j there is no-one no student respects Jay

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7 (Sx & Rjx) xx x is a S and j R's x there is someone x who is a S and whom j R's who is a S (whom) j respects there is someone Jay respects some (at least one) student

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8 x respects every politician xx there is no x : who respects every politicianthere is no one no-one respects every politician

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9 IF y is P, THEN x R’s yno matter who y is xx x y ( Py Rxy ) y ( Py Rxy ) Py Rxy yy IF you are P, THEN x R’s youno matter who you are x respects every politician

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10 x ( Sx x R's someone ) Sx x R's someone xx IF x is S, THEN x R's someoneno matter who x is IF you are S, THEN you R someoneno matter who you are every Student respects someone or other

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11 x ( Sx y Rxy ) Rxy yy x R's ythere is some y whom x R's who is R'ed by x there is someone ) x R's someone x ( Sx

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12 Px & no-one R's x xx x is P AND no-one R's xthere is some x : who is P AND whom no-one R's who is a P whom no-one R‘s there is someone there is a politician whom no-one respects x ( Px & no-one R's x )

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13 x ( Px & y Ryx ) Ryx yy y R's xthere is no y who R’s xthere is no one ) no one R's x x ( Px &

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14 Px & every C R's x xx x ( Px & every C R's x ) x is P AND every C R's xthere is some x who is P AND whom every C R's who is a P whom every C R's there is someone there is a Politician whom every Citizen Respects

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15 x ( Px & y ( Cy Ryx ) ) y ( Cy Ryx ) Cy Ryx yy if y is C then y R’s xno matter who y is if you are C then you R xno matter who you are ) every C R's x x ( Px &

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16 Cx x R's some P xx x ( Cx x R's some P ) if x is C, then x R's some Pno matter who x is if you are C, then you R some Pno matter who you are every Citizen Respects some Politician (or other)

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17 x ( Cx y ( Py & Rxy ) ) y ( Py & Rxy ) Py & Rxy yy y is P AND x R's y there is some y who is P AND whom x R's who is a P AND who is R'ed by x who is a P R'ed by x there is someone ) x R's some P x ( Cx

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18 Cx & x R's no P xx x ( Cx & x R's no P ) x is a C AND x R's no Pthere is some x : who is a C AND who R's no P who is a C who R's no P there is someone there is a Citizen who Respects no Politician

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19 x ( Cx & y ( Py & Rxy ) ) y ( Py & Rxy ) Py & Rxy yy y is P AND x R's y y is P AND y is R’ed by x there is no y : who is a P AND who is R'ed by x there is no one ) x R's no P x ( Cx &

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1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

1 Copyright © 2010, Elsevier Inc. All rights Reserved Fig 2.1 Chapter 2.

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