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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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) )