with an Entity-Premiss.]

30. No muffins are wholesome;
All puffy food is unwholesome.
All muffins are puffy.

Univ. is "food"; m = wholesome; x = muffins; y = puffy.

xm_{0} + y_{1}m_{0}

No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]

31. No birds, except peacocks, are proud of their tails;
Some birds, that are proud of their tails, cannot sing.
Some peacocks cannot sing.

Univ. "birds"; m = proud of their tails; x = peacocks; y = birds that
cannot sing.

x'm_{0} + my'_{1} > xy'_{1} [Fig. II.

Conclusion right.

32. Warmth relieves pain;
Nothing, that does not relieve pain, is useful in toothache.
Warmth is useful in toothache.

Univ. "applications"; m = relieving pain; x = warmth; y = useful in
toothache.

x_{1}m'_{0} + m'y_{0}

No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]

33. No bankrupts are rich;
Some merchants are not bankrupts.
Some merchants are rich.

Univ. "persons"; m = bankrupts; x = rich; y = merchants.

mx_{0} + ym'_{1}

No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]

34. Bores are dreaded;
No bore is ever begged to prolong his visit.
No one, who is dreaded, is ever begged to prolong his visit.

Univ. "persons"; m = bores; x = dreaded; y = begged to prolong their
visits.

m_{1}x'_{0} + my_{0} > xy'_{1} [Fig. III.

Conclusion wrong: the right one is "Some dreaded persons are not begged
to prolong their visits."

35. All wise men walk on their feet;
All unwise men walk on their hands.
No man walks on both.

Univ. "men"; m = wise; x = walking on their feet; y = walking on their
hands.

m_{1}x'_{0} + m'_{1}y'_{0} > x'y'_{0} [Fig. I.

Conclusion wrong: right one is "No man walks on neither."
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36. No wheelbarrows are comfortable;
No uncomfortable vehicles are popular.
No wheelbarrows are popular.

Univ. "vehicles"; m = comfortable; x = wheelbarrows; y = popular.

xm_{0} + m'x_{0} > xy_{0} [Fig. I.

Conclusion right.

37. No frogs are poetical;
Some ducks are unpoetical.
Some ducks are not frogs.

Univ. "creatures"; m = poetical; x = frogs; y = ducks.

xm_{0} + ym'_{1}

No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]

38. No emperors are dentists;
All dentists are dreaded by children.