Phil 120 week 1 class 1 July 5th 2004

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 doesnt 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 doesnt 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(LsxLrx ? Lmx)
• 3 Michael likes everyone that either Sue or Rita
  like
• 4 Rita doesnt 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(LsxLrx ? Lmx)
• Michael likes everyone that either Sue or Rita
  like
• ?x(Lsx?Lrx ? Lmx)
• 4 Rita doesnt 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(LsxLrx ? Lmx)
• Michael likes everyone that either Sue or Rita
  like
• ?x(Lsx?Lrx ? Lmx)
• Rita doesnt 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(LsxLrx ? Lmx)
• Michael likes everyone that either Sue or Rita
  like
• ?x(Lsx?Lrx ? Lmx)
• Rita doesnt 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(LsxLrx ? Lmx)
• Michael likes everyone that either Sue or Rita
  like
• ?x(Lsx?Lrx ? Lmx)
• Rita doesnt 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(LsxLrx ? Lmx)
• Michael likes everyone that either Sue or Rita
  like
• ?x(Lsx?Lrx ? Lmx)
• Rita doesnt 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
doesnt like everyone 15 Michael doesnt 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 doesnt like everyone
• 15 Michael doesnt 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 doesnt like everyone
• 15 Michael doesnt 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 doesnt like everyone
• 15 Michael doesnt 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 doesnt like everyone
• 15 Michael doesnt 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 doesnt like everyone ?xLmx
• 15 Michael doesnt 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 doesnt like everyone ?xLmx
• 15 Michael doesnt 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 doesnt like everyone ?xLmx
• 15 Michael doesnt 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 doesnt like everyone ?xLmx
• 15 Michael doesnt 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
cats-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 cats-eyes belong to
Rhoda 19 All the marbles but the shooters are
cats-eyes 20 Some but not all of the cats-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
• 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

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
• 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
• 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

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
• 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 ? yx) )
• 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

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
• 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 ? yx) )
• There are at least two apples in the basket
• ?x?y(Ax Nxb Ay Nyb
• 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

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
• 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 ? yx) )
• 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
• There are no more than two pears in the basket
• 47 there 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
• 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 ? yx) )
• 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 ?z(Az Nzb ? (zy ?
  zx) x?y )
• There are no more than two pears in the basket
• 47 there 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
• 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 ? yx) )
• 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 ?z(Az Nzb ? (zy ?
  zx) x?y )
• There are no more than two pears in the basket
• ?x?y(Ax Nxb Ay Nyb ?z(Az Nzb ? (zy ?
  zx) )
• 47 there 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
• 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 ? yx) )
• There are at least two apples in the basket
• ?x?y(Ax Nxb Ay Nyb
• There are two (and only two) apples in the basket
• ?x?y(Ax Nxb Ay Nyb ?z(Az Nzb ? (zy ?
  zx) )
• There are no more than two pears in the basket
• ?x?y(Ax Nxb Ay Nyb ?z(Az Nzb ? (zy ?
  zx) )
• there are at least three apples in the basket
• ?x?y?z (Ax Ay Az Nxb Nyb Nzb
• ?w(Aw Nwb ? wx ? wy ? wz) )