# Logical Venn Diagrams: Exercise-1

Directions (1-10): In each of the following questions two or three statements followed by two conclusions are given. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

(1-2): Statements:

Some pens are pencils.

All pencils are books.

Some books are boxes.

1. Conclusions:

(I). All boxes being pencils is a possibility.
(II). At least some boxes are pens.

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 boxes being pencils but at least some boxes are pens not follow the statements, so only conclusion (I) follows.

1. Conclusions:

(I). Some books are pens.
(II). All books are pens.

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:
Only first conclusion 'Some books are pens' follows the statements, but the second conclusion 'All books are pens' is not possible.

1. Statements:

Some tables are chairs.
No chair is a bed.
All shoes are beds.

Conclusions:

(I). No shoe is a chair.
(II). Some tables are definitely not beds.

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. Statements:

All trees are plants.
Some plants are leafs.
Some leafs are roots.

Conclusions:

(I). No root is a tree.
(II). All leafs being trees 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:
It is possible that all leafs being trees, but the first conclusion 'No root is a tree' not follows the statements.

1. Statements:

No women is a girl.
Some womens are Indians.

Conclusions:

(I). No Indian is a girl.
(II). Some Indians 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: (b) If either conclusion I or conclusion II follows.

Solution:
From the two given conclusions, only one conclusion can follow the statements, eather I or II.

(6-7): Statements:

All mobiles are laptops.

Some laptops are tablets.

Some tablets are Smartwatches

1. Conclusions:

(I). All tablets being mobiles is a possibility.
(II). No smartwatch is a laptop.

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 tablets being mobiles, but conclusion second 'No smartwatch is a laptop' is not following the statements.

1. Conclusions:

(I). All laptops are mobiles.
(II). No mobile is a smartwatch.

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:

Some trains are buses.
Some buses are cars.
All cars are bicycles

Conclusions:

(I). All trains being bicycles is a possibility.
(II). At least some buses are bicycles.

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. Statements:

Some songs are stories.
No story is a movie.

Conclusions:

(I). Some songs are movies.
(II). No song is a movie.

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: (b) If either conclusion I or conclusion II follows.

Solution:
From the two given conclusions, only one conclusion can follow the statements, eather I or II.

1. Statements:

No cup is a plate.
All plates are pans.
Some pans are spoons.

Conclusions:

(I). No cup is a spoon.
(II). At least some cups are pans.

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 cups are pans, but the first conclusion 'No cup is a spoon' not follows the statements.