1. 1Everyone that Michael likes likes either Henry or Sue 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita like 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

2. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like 3Michael likes everyone that either Sue or Rita like 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

3. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

4. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

5. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

6. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not  x(Gx  Dx) &  x(Bx  ~Dx) 6Grizzly bears and polar bears are dangerous but black bears are not 7Every self-respecting polar bear is a good swimmer

7. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not  x(Gx  Dx) &  x(Bx  ~Dx) 6Grizzly bears and polar bears are dangerous but black bears are not  x(Gx  Px  Dx) &  x(Bx  ~Dx) 7Every self-respecting polar bear is a good swimmer

8. 1Everyone that Michael likes likes either Henry or Sue  x(Lmx  Lxs  Lxh) 2Michael likes everyone that both Sue and Rita like  x(Lsx&Lrx  Lmx) 3Michael likes everyone that either Sue or Rita like  x(Lsx  Lrx  Lmx) 4Rita doesn’t like Michael but she likes everyone that Michael likes ~Lrm &  x(Lmx  Lrx) 5Grizzly bears are dangerous but black bears are not  x(Gx  Dx) &  x(Bx  ~Dx) 6Grizzly bears and polar bears are dangerous but black bears are not  x(Gx  Px  Dx) &  x(Bx  ~Dx) 7Every self-respecting polar bear is a good swimmer  x(Px & Rxx  Sx)

9. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita 11If anyone likes Sue, Michael does 12If everyone likes Sue, Michael does 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

10. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does 12If everyone likes Sue, Michael does 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

11. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

12. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

13. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

14. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

15. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone~  xLmx 16If someone likes Sue, then s/he likes Rita 17If someone likes Sue, then someone likes Rita

16. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone~  xLmx 16If someone likes Sue, then s/he likes Rita  x(Lxs  Lxr) 17If someone likes Sue, then someone likes Rita

17. UD = people 9Anyone who likes Sue likes Rita  x(Lxs  Lxr) 10Everyone who likes Sue likes Rita the same as 9 11If anyone likes Sue, Michael does  xLxs  Lms 12If everyone likes Sue, Michael does  xLxs  Lms 13If anyone likes Sue, he or she likes Rita  x(Lxs  Lxr) 14Michael doesn’t like everyone~  xLmx 15Michael doesn’t like anyone~  xLmx 16If someone likes Sue, then s/he likes Rita  x(Lxs  Lxr) 17If someone likes Sue, then someone likes Rita  xLxs   xLxr

18. For 18-28: UD: Ashley, Rhoda, Terry, Clarence and their marbles a, r, t, c stand for Ashley, Rhoda, Terry, Clarence respectively Bxx is blue Gxx is green Rxx is red Sxx is a shooter Cxx is a cat’s-eye Txx is a steely Mx x is a marble Bxyx belongs to y Wxyx wins y Gxyzx gives y to z 18All the cat’s-eyes belong to Rhoda 19All the marbles but the shooters are cat’s-eyes 20Some but not all of the cat’s-eyes are green 21None of the steelies is red green or blue

19. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket 43The only pear in the basket is rotten 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

20. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

21. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

22. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

23. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

24. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb & x  y ) 45There are two (and only two) apples in the basket 46There are no more than two pears in the basket 47there are at least three apples in the basket

25. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb & x  y ) 45There are two (and only two) apples in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) & x  y ) 46There are no more than two pears in the basket 47there are at least three apples in the basket

26. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb & x  y ) 45There are two (and only two) apples in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) & x  y ) 46There are no more than two pears in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) ) 47there are at least three apples in the basket

27. For 42 – 47: UD = everything; Ax = x is an apple; Nxy = x is in y; Px = x is a pear; Rx = x is rotten; b = the basket 42There are apples and pears in the basket  x(Px & Nxb) &  x(Ax & Nxb) 43The only pear in the basket is rotten  x(Px & Nxb & Rx &  y(Py & Nyb  y=x) ) 44There are at least two apples in the basket  x  y(Ax & Nxb & Ay & Nyb 45There are two (and only two) apples in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) ) 46There are no more than two pears in the basket  x  y(Ax & Nxb & Ay & Nyb &  z(Az & Nzb  (z=y  z=x) ) 47there are at least three apples in the basket  x  y  z (Ax & Ay & Az & Nxb & Nyb & Nzb & &  w(Aw & Nwb  w=x  w=y  w=z) )