1everyone that michael likes likes either henry or sue 2michael likes everyone that both sue and...

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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

2 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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

2 Michael likes everyone that both Sue and Rita like

x(Lsx&Lrx Lmx)

3 Michael likes everyone that either Sue or Rita like

x(LsxLrx 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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

2 Michael likes everyone that both Sue and Rita like

x(Lsx&Lrx Lmx)

3 Michael likes everyone that either Sue or Rita like

x(LsxLrx Lmx)

4 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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

2 Michael likes everyone that both Sue and Rita like

x(Lsx&Lrx Lmx)

3 Michael likes everyone that either Sue or Rita like

x(LsxLrx Lmx)

4 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

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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

2 Michael likes everyone that both Sue and Rita like

x(Lsx&Lrx Lmx)

3 Michael likes everyone that either Sue or Rita like

x(LsxLrx Lmx)

4 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

x(Gx Dx) & x(Bx ~Dx)

2 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

1 Everyone that Michael likes likes either Henry or Sue

x(Lmx LxsLxh)

2 Michael likes everyone that both Sue and Rita like

x(Lsx&Lrx Lmx)

3 Michael likes everyone that either Sue or Rita like

x(LsxLrx Lmx)

4 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

x(Gx Dx) & x(Bx ~Dx)

2 Grizzly bears and polar bears are dangerous but black bears are not

x(Gx Px Dx) & x(Bx ~Dx)

3 Every self-respecting polar bear is a good swimmer

x(Px & Rxx Sx)

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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 If anyone likes Sue, Michael does

xLxs Lms

12 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 If anyone likes Sue, Michael does

xLxs Lms

12 If everyone likes Sue, Michael does

xLxs Lms

13 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 If anyone likes Sue, Michael does

xLxs Lms

12 If everyone likes Sue, Michael does

xLxs Lms

13 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 If anyone likes Sue, Michael does

xLxs Lms

12 If everyone likes Sue, Michael does

xLxs Lms

13 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 If anyone likes Sue, Michael does

xLxs Lms

12 If everyone likes Sue, Michael does

xLxs Lms

13 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

UD = people

9 Anyone who likes Sue likes Rita

x(Lxs Lxr)

10 Everyone who likes Sue likes Rita

the same as 9

11 If anyone likes Sue, Michael does

xLxs Lms

12 If everyone likes Sue, Michael does

xLxs Lms

13 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

For 18-28:UD: Ashley, Rhoda, Terry, Clarence and their marblesa, r, t, c stand for Ashley, Rhoda, Terry, Clarence respectively

Bx x is blueGx x is greenRx x is redSx x is a shooterCx x is a cat’s-eyeTx x is a steelyMx x is a marbleBxy x belongs to yWxy x wins yGxyz x gives y to z

18 All the cat’s-eyes belong to Rhoda 19 All the marbles but the shooters are cat’s-eyes20 Some but not all of the cat’s-eyes are green21 None of the steelies is red green or blue

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

42 There are apples and pears in the basket

43 The only pear in the basket is rotten

44 There are at least two apples in the basket

45 There are two (and only two) apples in the basket

46 There are no more than two pears in the basket

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rotten

44 There are at least two apples in the basket

45 There are two (and only two) apples in the basket

46 There are no more than two pears in the basket

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx

44 There are at least two apples in the basket

45 There are two (and only two) apples in the basket

46 There are no more than two pears in the basket

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx & y(Py & Nyb y=x) )

44 There are at least two apples in the basket

45 There are two (and only two) apples in the basket

46 There are no more than two pears in the basket

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx & y(Py & Nyb y=x) )

44 There are at least two apples in the basketxy(Ax & Nxb & Ay & Nyb

45 There are two (and only two) apples in the basket

46 There are no more than two pears in the basket

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx & y(Py & Nyb y=x) )

44 There are at least two apples in the basketxy(Ax & Nxb & Ay & Nyb & xy )

45 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

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx & y(Py & Nyb y=x) )

44 There are at least two apples in the basketxy(Ax & Nxb & Ay & Nyb & xy )

45 There are two (and only two) apples in the basketxy(Ax & Nxb & Ay & Nyb & z(Az & Nzb (z=y z=x) & xy )

• There are no more than two pears in the basket

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx & y(Py & Nyb y=x) )

44 There are at least two apples in the basketxy(Ax & Nxb & Ay & Nyb & xy )

45 There are two (and only two) apples in the basketxy(Ax & Nxb & Ay & Nyb & z(Az & Nzb (z=y z=x) & xy )

• There are no more than two pears in the basketxy(Ax & Nxb & Ay & Nyb & z(Az & Nzb (z=y z=x) )

47 there are at least three apples in the basket

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

42 There are apples and pears in the basketx(Px & Nxb) & x(Ax & Nxb)

43 The only pear in the basket is rottenx(Px & Nxb & Rx & y(Py & Nyb y=x) )

44 There are at least two apples in the basketxy(Ax & Nxb & Ay & Nyb

45 There are two (and only two) apples in the basketxy(Ax & Nxb & Ay & Nyb & z(Az & Nzb (z=y z=x) )

• There are no more than two pears in the basketxy(Ax & Nxb & Ay & Nyb & z(Az & Nzb (z=y z=x) )

• there are at least three apples in the basketxyz (Ax & Ay & Az & Nxb & Nyb & Nzb &

& w(Aw & Nwb w=x w=y w=z) )