Complete Works of Lewis Carroll (182 page)

There is no Conclusion.

  9.
John is in the house;

Everybody in the house is ill.

Univ.
is “persons”;
m
 = persons in the house;
x
 = the Class of Johns;
y
 = ill.

All
x
are
m
;

All
m
are
y
.

∴
All
x
are
y
.

i.e.
John is ill.

10.
Umbrellas are useful on a journey;

What is useless on a journey should be left behind.

Univ.
is “things”;
m
 = useful on a journey;
x
 = umbrellas;
y
 = things that should be left behind.

All
x
are
m
;

All
m
′
are
y
.

∴
Some
x
′
are
y
.

i.e.
Some things, that are not umbrellas, should be left behind on a journey.

11.
Audible music causes vibration in the air;

Inaudible music is not worth paying for.

Univ.
is “music”;
m
 = audible;
x
 = music that causes vibration in the air;
y
 = worth paying for.

All
m
are
x
;

All
m
′
are
y
′
.

∴
No
x
′
are
y
.

i.e.
No music is worth paying for, unless it causes vibration in the air.

12.
Some holidays are rainy;

Rainy days are tiresome.

Univ.
is “days”;
m
 = rainy;
x
 = holidays;
y
 = tiresome.

Some
x
are
m
;

All
m
are
y
.

∴
Some
x
are
y
.

i.e.
Some holidays are tiresome.

SL6-A
Solutions for § 6, Nos.
1
–10.

  1.

Some
x
are
m
; No
m
are
y
′
.
Some
x
are
y
.