I.
State each of the following in 3 equivalent forms:—
(1) There are no perfect men.
(2) Some apples are unripe.
(3) No pigs can fly.
II.
Taking x = ‘good riddles,’ and y = ‘hard,’ interpret:—
(1). (2).
(3). (4).
III.
Break up each of the following into its 2 component propositions:—
(1) All judges are just.
(2) All good children are happy.
(3) All old and sickly men are fretful and troublesome.
IV.
Taking x = ‘cakes,’ and y = ‘wholesome,’ represent, with diagrams like those in Qu. II, the following propositions:—
(1) Some cakes are unwholesome.
(2) There are no wholesome cakes.
(3) There are no cakes in existence.
(4) All cakes are wholesome.
V.
Taking x = ‘diligent students,’ and y = ‘successful,’ represent in like manner:—
(1) No diligent students are unsuccessful.
(2) All diligent students are successful.
(3) There are some diligent students.
(4) There are some diligent, but unsuccessful, students.
[June, 1886.]