# Logical Venn Diagrams: Exercise-2

1. Statements:

All plastics are steels.
All steels are irons.
No iron is a liquid.

Conclusions:

(I). All irons are steels.
(II). All plastics are irons.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (e) If only conclusion II follows.

Solution:
The first conclusion 'All irons are steels' is not possible but the second conclusion 'All plastics are irons' is possible.

1. Statements:

No apple is a banana.
All grapes are bananas.
Some apples are mangoes.

Conclusions:

(I). Some mangoes are grapes.
(II). Some grapes being apples is a possibility.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (a) If neither conclusion I nor conclusion II follows.

Solution:
No conclusion is following the statements.

1. Statements:

All fans are coolers.

Conclusions:

(I). All coolers are fans.
(II). Some radios being fans is a possibility.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (e) If only conclusion II follows.

Solution:
The first conclusion 'All coolers are fans' is not possible but it is possible that Some radios being fans.

(4-5): Statements:

No bird is an animal.

All animal are monkeys.

Some monkeys are lions.

1. Conclusions:

(I). At least some animals are lions.
(II). All birds being lions is a possibility.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (d) If both the conclusion I and conclusion II follows.

Solution:
Folllow the figure given above.

1. Conclusions:

(I). All monkeys can never be birds.
(II). Some lions are definitely not birds.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (a) If neither conclusion I nor conclusion II follows.

Solution:
No conclusion is following the statements.

(6-7): Statements:

All flowers are fruits.

Some fruits are mangoes.

Some mangoes are apples.

1. Conclusions:

(I). All flowers can never be mangoes.
(II). At least some apples are fruits.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (e) If only conclusion II follows.

Solution:
It is possible that at least some apples are fruits, but the first conclusion 'All flowers can never be mangoes' not follows the statements.

1. Conclusions:

(I). All flowers being apples is a possibility.
(II). No fruit is a apple.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (c) If only conclusion I follows.

Solution:
It is possible that all flowers being apples, but the second conclusion 'No fruit is a apple' not follows the statements.

(8-10): Statements:

All boys are girls.

All girls are womwn.

1. Conclusions:

(I). Some women are boys.
(II). Some girls are boys.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (d) If both the conclusion I and conclusion II follows.

Solution:
Both the conclusions are following the statements.

1. Conclusions:

(I). All boys are women.
(II). Some boys are not girls.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (c) If only conclusion I follows.

Solution:
It is possible that all boys are women, but the second conclusion 'Some boys are not girls' not follows the statements.

1. Conclusions:

(I). All girls are boys.
(II). Some women are girls.

1. If neither conclusion I nor conclusion II follows.
2. If either conclusion I or conclusion II follows.
3. If only conclusion I follows.
4. If both the conclusion I and conclusion II follows.
5. If only conclusion II follows.

Answer: (e) If only conclusion II follows.

Solution:
It is possible that some women are girls, but the first conclusion 'All girls are boys' not follows the statements.