[pg141]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.