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1 Everyone that Michael likes likes either Henry or Sue

1 Everyone that Michael likes likes either Henry or Sue 2 Michael likes everyone that both Sue and Rita like 3 Michael likes everyone that either Sue or Rita like 4 Rita doesn’t like Michael but she likes everyone that Michael likes 5 Grizzly bears are dangerous but black bears are not

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1 Everyone that Michael likes likes either Henry or Sue

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  17. UD = people • 9 Anyone who likes Sue likes Rita • x(Lxs  Lxr) • Everyone who likes Sue likes Rita • the same as 9 • If anyone likes Sue, Michael does • xLxs  Lms • If everyone likes Sue, Michael does • xLxs  Lms • If anyone likes Sue, he or she likes Rita • x(Lxs  Lxr) • 14 Michael doesn’t like everyone ~xLmx • 15 Michael doesn’t like anyone ~xLmx • 16 If someone likes Sue, then s/he likes Rita x(Lxs  Lxr) • 17 If 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 Bx x is blue Gx x is green Rx x is red Sx x is a shooter Cx x is a cat’s-eye Tx x is a steely Mx x is a marble Bxy x belongs to y Wxy x wins y Gxyz x gives y to z 18 All the cat’s-eyes belong to Rhoda 19 All the marbles but the shooters are cat’s-eyes 20 Some but not all of the cat’s-eyes are green 21 None 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 • There are apples and pears in the basket • The only pear in the basket is rotten • There are at least two apples in the basket • There are two (and only two) apples in the basket • There are no more than two pears in the basket • 47 there 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 • There are apples and pears in the basket • x(Px & Nxb) & x(Ax & Nxb) • The only pear in the basket is rotten • x(Px & Nxb & Rx& y(Py & Nyb  y=x) ) • There are at least two apples in the basket • xy(Ax & Nxb & Ay & Nyb & xy) • There are two (and only two) apples in the basket • xy(Ax & Nxb & Ay & Nyb & xy & z(Az & Nzb  (z=y  z=x) ) • There are no more than two pears in the basket • xy(Ax & Nxb & Ay & Nyb & z(Az & Nzb  (z=y  z=x) ) • there are at least three apples in the basket • xyz (Ax & Ay & Az & Nxb & Nyb & Nzb & xy& xz& zy & w(Aw & Nwb  w=x  w=y  w=z) )

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