Some m are x; &there4 Some x are y. All xm are y. i.e. Some rainy periods are tiresome. N.B. These are not legitimate Premisses, since the Conclusion is really part of the second Premiss, so that the first Premiss is superfluous. This may be shown, in letters, thus:-- "All xm are y" contains "Some xm are y", which contains "Some x are y". Or, in words, "All rainy days are tiresome" contains "Some rainy days are tiresome", which contains "Some rainy periods are tiresome". Moreover, the first Premiss, besides being superfluous, is actually contained in the second; since it is equivalent to "Some rainy days exist", which, as we know, is implied in the Proposition "All rainy days are tiresome". Altogether, a most unsatisfactory Pair of Premisses! --------------- | 0 | | | ---|--- | | | 1 | | | 20. |---|---|---|---| ------- | | 0 | 0 | | | 1 | | | ---|--- | |---|---| | 0 | | | 0 | | --------------- ------- Let "things" be Universe; m="medicine"; x="nasty"; y="senna". All m are x; &there4 All y are x. All y are m. i.e. Senna is nasty. [See remarks on No. 7, p 60.] --------------- | | | | ---|--- | | | 0 | 1 | | 21. |-1-|---|---|---| ------- | | 0 | | | | | 1 | | ---|--- | |---|---| | | | | | | --------------- ------- Let "persons" be Universe; m="Jews"; x="rich"; y="Patagonians". Some m are x; &there4 Some x are y'. All y are m'. i.e. Some rich persons are not Patagonians. --------------- | 0 | | | ---|--- | | | - | | 22. |---|---|---|---| ------- | | 0 | 0 | | | | | | ---|--- | |---|---| | 0 | | | 0 | | --------------- ------- Let "creatures" be Universe; m="teetotalers"; x="that like sugar"; y="nightingales". All m are x; &there4 No y are x'. No y are m'. i.e. No nightingales dislike sugar. --------------- | | | | ---|--- | | | 0 | 0 | | 23. |-1-|---|---|---| ------- | | 0 | | | | | | | ---|--- | |---|---| | | | | | | --------------- ------- Let "food" be Universe; m="wholesome"; x="muffins"; y="buns". No x are m; All y are m. There is 'no information' for the smaller Diagram; so no Conclusion can be drawn.