No emperors are dreaded by children.

Univ. "persons"; m = dentists; x = emperors; y = dreaded by children.

xm_{0} + m_{1}y'_{0} > x'y_{1} [Fig. III.

Conclusion wrong: right one is "Some persons, dreaded by children, are
not emperors."

39. Sugar is sweet;
Salt is not sweet.
Salt is not sugar.

Univ. "things"; m = sweet; x = sugar; y = salt.

x_{1}m'_{0} + y_{1}m_{0} > (x_{1}y_{0} + y_{1}x_{0}) [Fig. I (b).

Conclusion incomplete: omitted portion is "Sugar is not salt."

40. Every eagle can fly;
Some pigs cannot fly.
Some pigs are not eagles.

Univ. "creatures"; m = creatures that can fly; x = eagles; y = pigs.

x_{1}m'_{0} + ym'_{1} > x'y_{1} [Fig. II.

Conclusion right.

_Solutions for Sec. 8._ SL8

1 2 3
1. cd_{0} + a_{1}d'_{0} + b_{1}c'_{0};

1 2 3
cd + ad' + bc' > ab_{0} + a_{1} + b_{1}
-- = =

i.e. > a_{1}b_{0} + b_{1}a_{0}

1 2 3
2. d_{1}b'_{0} + ac'_{0} + bc_{0};

1 3 2
db' + bc + ac' > da_{0} + d_{1} i.e. > d_{1}a_{0}
- =- =

1 2 3
3. ba_{0} + cd'_{0} + d_{1}b'_{0};

1 3 2
ba + db' + cd' > ac_{0}
- -= =

1 2 3
4. bc_{0} + a_{1}b'_{0} + c'd_{0};

1 2 3
bc + ab' + c'd > ad_{0} + a_{1} i.e. > a_{1}d_{0}
-- = =
pg156
1 2 3 1 2 3
5. b'_{1}a_{0} + bc_{0} + a'd_{0}; b'a + bc + a'd > cd_{0}
- - = =

1 2 3
6. a_{1}b_{0} + b'c_{0} + d_{1}a'_{0};

1 2 3
ab + b'c + da' > cd_{0} + d_{1} i.e. > d_{1}c_{0}
-- = =

1 2 3 1 2 3
7. db'_{0} + b_{1}a'_{0} + cd'_{0}; db' + ba' + cd' > a'c_{0}
-- = =

1 2 3
8. b'd_{0} + a'b_{0} + c_{1}d'_{0};

1 2 3
b'd + a'b + cd' > a'c_{0} + c_{1} i.e. > c_{1}a'_{0}
- - = =

1 2 3
9. b'_{1}a'_{0} + ad_{0} + b_{1}c'_{0};

1 2 3
b'a' + ad + bc' > dc'_{0}
- - = =

1 2 3
10. cd_{0} + b_{1}c'_{0} + ad'_{0};

1