Deriving Conclusion examples

1.Statements:

• Some stones are cubes.
• No cube is a glass.
• All bats are cubes.

Conclusions:

1. Some stones being bats is a possibility.
2. No bat is a glass.
3. All cubes are bats.
4. No stone is a glass.

Options:

1. Only Conclusions I, II, and IV follow
2. Only Conclusions II and III follow
3. Only Conclusions I and II follow
4. Only Conclusion I follows

Answer: Option 3: Only Conclusions I and II follow

Explanation:

• Conclusion I: Some stones being bats is a possibility because some stones are cubes, and all bats are cubes.
• Conclusion II: No bat is a glass because all bats are cubes, and no cube is a glass.
• Conclusion III: Does not follow because not all cubes are bats; only bats are cubes.
• Conclusion IV: Does not follow because there is no direct relationship between stones and glasses.

2. Statements:

• All roses are flowers.
• Some flowers are red.

Conclusions:

1. Some roses are red.
2. All red things are roses.
3. Some flowers are not roses.
4. Some roses are not red.

Options:

1. Only Conclusion I follows
2. Only Conclusion III follows
3. Only Conclusions I and III follow
4. Only Conclusion IV follows

Answer: Option 3: Only Conclusions I and III follow

Explanation:

• Conclusion I: Some roses can be red because all roses are flowers, and some flowers are red.
• Conclusion III: Some flowers are not roses because not all flowers are roses.
• Conclusion II: Does not follow because not all red things are roses; some red things are other flowers.
• Conclusion IV: Does not follow because some roses can be red.

3. Statements:

• All cats are animals.
• Some animals are pets.

Conclusions:

1. Some cats are pets.
2. All pets are cats.
3. Some cats are not pets.
4. Some pets are not cats.

Options:

1. Only Conclusion I follows
2. Only Conclusion III follows
3. Only Conclusions I and III follow
4. Only Conclusion IV follows

Answer: Option 3: Only Conclusions I and III follow

Explanation:

• Conclusion I: Some cats can be pets because all cats are animals, and some animals are pets.
• Conclusion III: Some cats are not pets because not all animals are pets.
• Conclusion II: Does not follow because not all pets are cats; some pets are other animals.
• Conclusion IV: Does not follow because some pets can be cats.

4.Statements:

• All birds can fly.
• Some birds are penguins.

Conclusions:

1. Some penguins can fly.
2. No penguin can fly.
3. All penguins are birds.
4. Some birds cannot fly.

Options:

1. Only Conclusion I follows
2. Only Conclusion II follows
3. Only Conclusion III follows
4. Only Conclusion IV follows

Answer: Option 4: Only Conclusion IV follows

Explanation:

• Conclusion IV: Some birds cannot fly because penguins are birds that cannot fly.
• Conclusion I: Does not follow because penguins are birds that cannot fly.
• Conclusion II: Does not follow because penguins are birds that cannot fly.
• Conclusion III: Does not follow because not all penguins are birds that can fly.

5.Statements:

• All fruits are sweet.
• Some fruits are mangoes.

Conclusions:

1. Some mangoes are sweet.
2. All mangoes are sweet.
3. Some fruits are not mangoes.
4. All sweet things are fruits.

Options:

1. Only Conclusion I follows
2. Only Conclusion I
3. Only Conclusion III follows
4. Only Conclusion I and III follow

Answer: Option 4: Only Conclusion I and III follow

Explanation:

• Conclusion I: True. Some mangoes are fruits, and since all fruits are sweet, some mangoes must be sweet.
• Conclusion III: True. Not all fruits are mangoes; there are other fruits besides mangoes.
• Conclusion II: False. The statement “Some fruits are mangoes” does not imply that all mangoes are sweet, though all fruits are.
• Conclusion IV: False. Not all sweet things are fruits; there could be sweet non-fruit items