CHAPTER VI.
1. Give the converse by negation of—
(1) All women are lovely.
(2) Some statesmen are not practical.
(3) All lawyers are honest.
(4) All doctors are skilful.
(5) Some men are not rational.
2. Give the contrapositive of—
(1) All solid substances are material.
(2) All the men who do not row play cricket.
(3) All impeccable beings are other than human,
(4) Some prejudiced persons are not dishonest.
3. Prove indirectly the truth of the contrapositive of 'All A is B.'
4. Criticise the following as immediate inferences—
(1) All wise men are modest.
.'. No immodest men are wise.
(2) Some German students are not industrious.
.'. Some industrious students are not Germans.
(3) Absolute difference excludes all likeness.
.'. Any likeness is a proof of sameness.
(4) None but the brave deserve the fair.
.'. All brave men deserve the fair.
(5) All discontented men are unhappy.
.'. No contented men are unhappy.
(6) Books being a source of instruction, our knowledge must come
from our libraries.
(7) All Jews are Semitic.
.'. Some non-Semitic people are not Jews.
5. Show by what kind of inference each of the subjoined propositions follows from
All discontented men are unhappy.
(1) All happy men are contented.
(2) Some discontented men are unhappy.
(3) Some contented men are happy.
(4) Some unhappy men are not contented.
(5) No discontented men are happy.
(6) Some happy men are contented.
(7) Some contented men are not unhappy.
(8) Some unhappy men are discontented.
(9) No happy men are discontented.
(10) Some discontented men are not happy.
(11) Some happy men are not discontented.
(12) None but unhappy men are discontented.
From how many of these propositions can the original one be derived?
And why not from all?