1everyone that michael likes likes either henry or sue 2michael likes everyone that both sue and...
Post on 22-Dec-2015
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![Page 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/1.jpg)
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
![Page 2: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/2.jpg)
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
![Page 3: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/3.jpg)
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
![Page 4: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/4.jpg)
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
![Page 5: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/6.jpg)
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
![Page 7: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/7.jpg)
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
![Page 8: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/8.jpg)
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)
![Page 9: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/9.jpg)
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
![Page 10: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/10.jpg)
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
![Page 11: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/11.jpg)
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
![Page 12: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/12.jpg)
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
![Page 13: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/13.jpg)
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
![Page 14: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/14.jpg)
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
![Page 15: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/15.jpg)
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
![Page 16: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/16.jpg)
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
![Page 17: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/17.jpg)
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
![Page 18: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/18.jpg)
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
![Page 19: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/19.jpg)
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
![Page 20: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/20.jpg)
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
![Page 21: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/21.jpg)
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
![Page 22: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/22.jpg)
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
![Page 23: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/23.jpg)
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
![Page 24: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/24.jpg)
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
![Page 25: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/25.jpg)
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
![Page 26: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/26.jpg)
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
![Page 27: 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](https://reader036.vdocuments.site/reader036/viewer/2022062516/56649d7d5503460f94a60490/html5/thumbnails/27.jpg)
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) )