## Syllogism

#### Syllogism

Direction: In each of the question below are Four statements following by Four conclusions numbered I, II, II and IV. You have to take the Four given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion logically follows from the two statements disregarding commonly known fact.

1. Statement:
Some doors are handles. All handles are pins. Some pins are threats. All threats are clothes.
Conclusions:
I. Some cloths are pins.
II. Some pins are doors.
III. Some clothes are handles.
IV. Some clothes are doors.

1. Some pins are threats + All threats are clothes = I + A = I = Some pins are clothes → conversion → Some clothes are pins (I) Hence I follows. Some doors are handles + All handles are pins = I + A = I = Some doors are pins → conversion → Some pins are doors (I) Hence II follows. All handles are pins + Some pins are clothes = I + A = No conclusion Hence III does not follow. Nor does IV follow consequently.

##### Correct Option: E

Some pins are threats + All threats are clothes = I + A = I = Some pins are clothes → conversion → Some clothes are pins (I) Hence I follows. Some doors are handles + All handles are pins = I + A = I = Some doors are pins → conversion → Some pins are doors (I) Hence II follows. All handles are pins + Some pins are clothes = I + A = No conclusion Hence III does not follow. Nor does IV follow consequently.

1. Statement:
Some days are nights. Some nights are weeks. Some weeks are months. All months are years.
Conclusions:
I. Some years are nights.
II. Some years are days.
III. Some months are nights.
IV. Some years are weeks.

1. Some nights are weeks + All weeks are months = I + A = I = Some nights are month → conversion → Some months are nights (I) Hence III follows. = Some nights are month + All months are years = I + A = I Some nights are year → conversion → Some years are nights (I) Hence I follows. All weeks are months + All months are years = A + A = A = All weeks are years → conversion → Some years are weeks (I) Hence IV follows. Some days are nights + Some nights are years = I + I = No conclusion Hence II does not follow.

##### Correct Option: B

Some nights are weeks + All weeks are months = I + A = I = Some nights are month → conversion → Some months are nights (I) Hence III follows. = Some nights are month + All months are years = I + A = I Some nights are year → conversion → Some years are nights (I) Hence I follows. All weeks are months + All months are years = A + A = A = All weeks are years → conversion → Some years are weeks (I) Hence IV follows. Some days are nights + Some nights are years = I + I = No conclusion Hence II does not follow.

1. Statement:
All dolls are toys. Some toys are gems. Some gems are boxes. All boxes are sticks.
Conclusions:
I. Some sticks are gems.
II. Some gems are dolls.
III. Some sticks are dolls.
IV. Some toys are dolls.

1. Some gems are boxes + All boxes are sticks = I + A = I = Some gems are sticks → Conversion → Some sticks are gems (I) Hence I follows All dolls are toys + Some toys are gems No conclusion Hence II and consequently III do not follow. All toys are dolls (A) → conversion → Some toys are dolls (I) Hence IV follows.

##### Correct Option: D

Some gems are boxes + All boxes are sticks = I + A = I = Some gems are sticks → Conversion → Some sticks are gems (I) Hence I follows All dolls are toys + Some toys are gems No conclusion Hence II and consequently III do not follow. All toys are dolls (A) → conversion → Some toys are dolls (I) Hence IV follows.

1. Statement:
Some sweets are chocolates. Some chocolates are mints. Some mints are food. Some food is diet.
Conclusions:
I. No sweets are diet.
II. No food is chocolates.
III. Some sweets are diet.
IV. Some sweets are food.

1. I-type statements can't be combined. However, I and III form a complementary I-E pair, Hence either I or III follows.

##### Correct Option: B

I-type statements can't be combined. However, I and III form a complementary I-E pair, Hence either I or III follows.

1. Statement:
All chairs are tables. All tables are desks. Some desks are benches. Some desks are sofas.
Conclusions:
I. Some benches are sofas.
II. Some sofas are tables.
III. Some benches are tables.
Iv. No chair is bench

1. Some desks are benches → (I) conversion → Some benches are desks (I) + Some desks are sofas = I + I = No conclusion Hence I does not follow. All tables are desks + Some desks are sofas = A + I = No conclusion Hence II does not follow. All tables are desks + Some desks are benches + A + I = No conclusion Hence III does not follow. For the same reason IV too does not follow.

##### Correct Option: A

Some desks are benches → (I) conversion → Some benches are desks (I) + Some desks are sofas = I + I = No conclusion Hence I does not follow. All tables are desks + Some desks are sofas = A + I = No conclusion Hence II does not follow. All tables are desks + Some desks are benches + A + I = No conclusion Hence III does not follow. For the same reason IV too does not follow.