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

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

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

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

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

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

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

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

9.  x ( Px    y Ryx ) Ryx yy y R's xthere is no y who R’s xthere is no one ) no one R's x  x ( Px &

10. xx there is some x there is some one there is a Politician who Respects every Citizen AND x respects every C  Px ) ( who is a politician who respects every C AND x is a politician x respects every C  x ( Px  x respects every C )

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

12. xx no matter who x is IF no matter who you are every Citizen Respects some Politician (or other) THEN x respects some P  Cx ) ( you are a citizen you respect some P IF THEN x is a citizen x respects some P  x ( Cx  x respects some P )

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

14. xx there is some x there is some one there is a Politician whom every Citizen Respects AND every C respects x  Px )( who is a politician whom every C respects AND x is a politician every C respects x  x ( Px  every C respects x )

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

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

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