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Syllogism 233
= A + A = A = All chairs are cushions Hence IV = I + I = No conclusion Hence I does not follow.
follows All tables are cushions + Some cushions are All tables are desks + Some desks are sofas = A + I
trolleys = A + I = No conclusion Hence I does not = No conclusion Hence II does not follow. All tables
follow. All chairs are cushions + Some cushions are are desks + Some desks are benches = A + I = No
trolleys = A + I = No conclusion Hence II does not conclusion Hence III does not follow. For the same
follow. reason IV too does not follow.
6. (c) Some flowers are buds + All buds are leaves + All 12. (b) I-type statements can’t be combined. However, I
leaves are plants = (I + A) + A = I = Some flowers and III form a complementary I-E pair, Hence either
are plants → conversion → Some plants are flowers I or III follows.
(I). Hence I follows. Some roses are flowers + Some 13. (d) Some gems are boxes + All boxes are sticks = I
flowers are buds = I + I = No conclusion Hence II + A = I = Some gems are sticks → Conversion →
and IV do not follow by combination. Nor can III Some sticks are gems (I) Hence I follows All dolls are
follow. However, II and IV form a complementary toys + Some toys are gems No conclusion Hence II
I-E pair, Hence either II or IV follows. and consequently III do not follow. All toys are dolls
7. (a) Some books are journals + All journals are papers (A) → conversion → Some toys are dolls (I) Hence
= I + A = I = Some books are papers → conversion IV follows.
→ Some papers are books(I). Hence I follows. Some 14. (b) Some nights are weeks + All weeks are months
papers are Cards + All cards are boards = I + A = = I + A = I = Some nights are month → conversion
I = Some papers are boards. Hence II follows. All → Some months are nights (I) Hence III follows. =
journals are papers + Some papers are boards = Some nights are month + All months are years =
A + I = No conclusion Hence III does not follow. I + A = I Some nights are years → conversion →
Some books are papers + Some papers are boards. Some years are nights (I) Hence I follows. All weeks
= I + I = No conclusion Hence IV do not follows. are months + All months are years = A + A = A =
8. (d) Some grapes are apples + Some apples are All weeks are years → conversion → Some years are
bananas = I + I = No conclusion So we can’t move weeks (I) Hence IV follows. Some days are nights
any further for ‘ grape’ and this rules out I and II. + Some nights are years = I + I = No conclusion
Some apples are banana + All banana are guava = Hence II does not follow.
I + A = I = Some apples are guavas → conversion 15. (e) Some pins are threats + All threats are clothes
→ Some guavas are apples (I). Hence III follows All = I + A = I = Some pins are clothes → conversion
bananas are guavas + No guava is pomegranate = → Some clothes are pins (I) Hence I follows. Some
A + E = E = No bananas are pomegranates. Hence doors are handles + All handles are pins = I + A
IV follows. = I = Some doors are pins → conversion → Some
9. (d) All walls are floors + All floors are rooms = A + pins are doors (I) Hence II follows. All handles
A = A = All walls are rooms Hence I follows. Some are pins + Some pins are clothes = I + A = No
doors are walls + All walls are floors = I + A = I conclusion Hence III does not follow. Nor does IV
= Some doors are rooms → conversion → Some follow consequently.
rooms are doors (I). Hence II follows. Conversion 16. (e) I-type statements can’t be combined.
of I gives us III. Some doors are walls + All walls 17. (c) Some rollers are wheels + All wheels are mats
are floors = I + A = I = Some doors are floors → = I + A = I = Some rollers are mats → conversion
conversion → Some floors are doors (I) Hence IV → Some mats are rollers (I) Hence I follows. Some
follows
rollers are mats + Some mats are cars = I + I = No
10. (b) Some forks are bowls + All bowls are plates = conclusion Hence III does not follow. All belts are
I + A = I = Some forks are plates → conversion rollers (A) → conversion → Some rollers are belts (I)
→ Some plates are forks (I). Hence II follows. Some Hence IV follows. All belts are rollers + Some rollers
forks are plates + Some plates are utensils = I + are mats = I + A = No conclusion Hence II does not
I = No conclusion Hence I does not follow. Some follow.
spoons are forks + Some forks are plates = I + I = 18. (b) All flowers are jungles + All jungles are tubes =
= No conclusion Hence III and IV do not follow. A + A = A = All flowers are tubes → conversion →
11. (a) Some desks are benches → (I) conversion → Some tubes are flowers (I) Hence IV follows. Some
Some benches are desks (I) + Some desks are sofas
