Single Quantifier, Multiple Predicates

1. Single Quantifier, Multiple Predicates some Student Respects Jay there is some one who is a student AND who respects Jay there is some x x is a student AND x respects Jay x Sx (  Rxj ) x ( SxRxj )

2. Single Quantifier, Multiple Predicates every Student Respects Kay no matter who you are IF you are a student THEN you respect Kay no matter who x is IF x is a student THEN x respects Kay Sx Rxk ) x (  x ( Sx  Rxk )

3. Single Quantifier, Multiple Predicates Jay Respects no Student there is no one who is a student AND whom Jay respects there is no x x is a student AND Jay respects x  Rjx ) x Sx ( x ( SxRjx )

4. Multiple Quantifiers, Multiple Predicates every Student Respects someone or other no matter who you are IF you are a student THEN you respect someone no matter who x is IF x is a student THEN x respects someone  x Sx ( x respects someone ) x ( Sxx respects someone )

5. Multiple Quantifiers, Multiple Predicates x ( Sx  x R's someone ) there is someone whom x R's there is some y x R's y y Rxy x ( Sx y Rxy )

6. Multiple Quantifiers, Multiple Predicates no-one Respects every Politician there is no one who respects every politician there is no x : x respects every politician x x (x respects every politician)

7. Multiple Quantifiers, Multiple Predicates x x Respects every Politician no matter who you are IF you are P THEN x R’s you no matter who y is IF y is P THEN x R’s y  Rxy ) Py y ( x y ( Py  Rxy )

8. Multiple Quantifiers, Multiple Predicates there is a Politician whom no-one Respects there is some one who is a politician AND whom no-one respects there is some x x is a politician AND no-one respects x ( ) x Px  no-one R's x x ( Pxno-one R's x )

9. Multiple Quantifiers, Multiple Predicates x ( Px & no one R's x ) there is no one who R’s x there is no y y R's x y Ryx x ( Pxy Ryx )

10. Multiple Quantifiers, Multiple Predicates there is a Politicianwho Respects every Citizen there is some one who is a politician AND who respects every C there is some x x is a politician AND x respects every C x Px (  x respects every C ) x ( Pxx respects every C )

11. Multiple Quantifiers, Multiple Predicates x ( Px x R's every C ) no matter who you are IF you are C THEN x R’s you no matter who y is IF y is C THEN x R’s y Rxy ) y Cy (  x ( Pxy ( Cy Rxy ) )

12. Multiple Quantifiers, Multiple Predicates every CitizenRespects some Politician (or other) no matter who you are IF you are a citizen THEN you respect some P no matter who x is IF x is a citizen THEN x respects some P Cx  ( x x respects some P ) x ( Cxx respects some P )

13. Multiple Quantifiers, Multiple Predicates x ( Cx  x R's some Politician ) there is someone who is a P AND whom x R's there is some y y is a P AND x R's y y ( Py  Rxy ) x ( Cxy ( PyRxy ) )

14. Multiple Quantifiers, Multiple Predicates there is a Politicianwhom every Citizen Respects there is some one who is a politician AND whom every C respects there is some x x is a politician AND every C respects x x (  ) Px every C respects x x (Pxevery C respects x )

15. Multiple Quantifiers, Multiple Predicates x ( Px every C R's x ) no matter who you are IF you are C THEN you R x no matter who y is IF y is C THEN y R’s x ( y ) Cy Ryx  x (Pxy ( Cy Ryx ) )

16. Multiple Quantifiers, Multiple Predicates there is a Citizen who Respects no Politician there is some one who is a citizen AND who respects no P there is some x x is a citizen AND x respects no P x Cx (  x respects no P ) x ( Cxx respects no P )

17. Multiple Quantifiers, Multiple Predicates x ( Cx x R's no P ) there is no-one who is P AND whom x R's there is no y y is P AND x R’s y y Py Rxy ( & ) x ( Cxy ( PyRxy ) )