Complete Works of Lewis Carroll (180 page)

There is no Conclusion.

10. 

All
x
are
m
;

All
y
′
are
m
′
.

∴
All
x
are
y
;

     All
y
′
are
x
′
.

11. 

No
m
are
x
;

All
y
′
are
m
′
.

There is no Conclusion.

12. 

No
x
are
m
;

All
y
are
m
.

∴
All
y
are
x
′
.

SL5-A
Solutions for § 5, Nos.
1
–12.

  1.
I have been out for a walk;

I am feeling better.

Univ.
is “persons”;
m
 = the Class of I’s;
x
 = persons who have been out for a walk;
y
 = persons who are feeling better.

All
m
are
x
;

All
m
are
y
.

∴
Some
x
are
y
.

i.e.
Somebody, who has been out for a walk, is feeling better.

  2.
No one has read the letter but John;

No one, who has
not
read it, knows what it is about.

Univ.
is “persons”;
m
 = persons who have read the letter;
x
 = the Class of Johns;
y
 = persons who know what the letter is about.

No
x
′
are
m
;

No
m
′
are
y
.

∴
No
x
′
are
y
.

i.e.
No one, but John, knows what the letter is about.

  3.
Those who are not old like walking;

You and I are young.

Univ.
is “persons”;
m
 = old;
x
 = persons who like walking;
y
 = you and I.

All
m
′
are
x
;

All
y
are
m
′
.