1️⃣ Statements: Some cats are animals. All animals are mammals.
Conclusions:
(I) Some cats are mammals.
(II) All mammals are cats.
Step-by-Step Explanation
"Some cats are animals" means there's an overlap between cats and animals.
"All animals are mammals" means animals are a subset of mammals.
(I) "Some cats are mammals" is true because if cats overlap with animals, and animals are mammals, then some cats must be mammals.
(II) "All mammals are cats" is false because mammals are a larger set containing animals, not just cats.
Therefore, only conclusion I follows.
Answer: Only conclusion I follows. ✅
2️⃣ Statements: All books are pens. Some pens are pencils.
Conclusions:
(I) Some books are pencils.
(II) All pencils are books.
Step-by-Step Explanation
"All books are pens" means books are a subset of pens.
"Some pens are pencils" means there's an overlap between pens and pencils.
(I) "Some books are pencils" is uncertain because we don't know if the overlap between pens and pencils includes books.
(II) "All pencils are books" is false because pencils are only partially related to pens, and books are a subset of pens.
Therefore, neither conclusion follows.
Answer: Neither I nor II follows. ✅
3️⃣ Statements: All dogs are pets. Some pets are toys.
Conclusions:
(I) Some dogs are toys.
(II) All toys are dogs.
Step-by-Step Explanation
"All dogs are pets" means dogs are a subset of pets.
"Some pets are toys" means there's an overlap between pets and toys.
(I) "Some dogs are toys" is uncertain because we don't know if the overlap between pets and toys includes dogs.
(II) "All toys are dogs" is false because toys are only partially related to pets, and dogs are a subset of pets.
Therefore, neither conclusion follows.
Answer: Neither I nor II follows. ✅
4️⃣ Statements: Some fruits are vegetables. All vegetables are plants.
Conclusions:
(I) Some fruits are plants.
(II) All plants are vegetables.
Step-by-Step Explanation
"Some fruits are vegetables" means there's an overlap between fruits and vegetables.
"All vegetables are plants" means vegetables are a subset of plants.
(I) "Some fruits are plants" is true because if fruits overlap with vegetables, and vegetables are plants, then some fruits must be plants.
(II) "All plants are vegetables" is false because plants are a larger set containing vegetables, not just vegetables.
Therefore, only conclusion I follows.
Answer: Only conclusion I follows. ✅
5️⃣ Statements: All chairs are tables. No tables are desks.
Conclusions:
(I) No chairs are desks.
(II) Some desks are chairs.
Step-by-Step Explanation
"All chairs are tables" means chairs are a subset of tables.
"No tables are desks" means tables and desks have no overlap.
(I) "No chairs are desks" is true because if chairs are a subset of tables, and tables have no overlap with desks, then chairs also have no overlap with desks.
(II) "Some desks are chairs" is false because there's no overlap between tables (and thus chairs) and desks.
Therefore, only conclusion I follows.
Answer: Only conclusion I follows. ✅
6️⃣ Statements: Some rivers are oceans. All oceans are seas.
Conclusions:
(I) Some rivers are seas.
(II) No rivers are seas.
Step-by-Step Explanation
"Some rivers are oceans" means there's an overlap between rivers and oceans.
"All oceans are seas" means oceans are a subset of seas.
(I) "Some rivers are seas" is true because if rivers overlap with oceans, and oceans are seas, then some rivers must be seas.
(II) "No rivers are seas" is false because we've established some rivers are seas.
Therefore, only conclusion I follows.
Answer: Only conclusion I follows. ✅
7️⃣ Statements: Some cars are buses. Some buses are trucks.
Conclusions:
(I) Some cars are trucks.
(II) No cars are trucks.
Step-by-Step Explanation
"Some cars are buses" means there's an overlap between cars and buses.
"Some buses are trucks" means there's an overlap between buses and trucks.
(I) "Some cars are trucks" is uncertain because we don't know if the overlap between buses and trucks includes cars.
(II) "No cars are trucks" is also uncertain because we don't know if there's any overlap between cars and trucks.
Therefore, neither conclusion follows.
Answer: Neither I nor II follows. ✅
8️⃣ Statements: All pens are erasers. Some erasers are books. No books are copies.
Conclusions:
(I) Some erasers are not copies.
(II) Some pens are books.
(III) No pens are copies.
Step-by-Step Explanation
"All pens are erasers" means pens are a subset of erasers.
"Some erasers are books" means there's an overlap between erasers and books.
"No books are copies" means books and copies have no overlap.
(I) "Some erasers are not copies" is true because some erasers are books, and no books are copies.
(II) "Some pens are books" is uncertain because we don't know if the overlap between erasers and books includes pens.
(III) "No pens are copies" is uncertain because we don't know if pens overlap with copies.
Therefore, only conclusion I follows.
Answer: Only I and II follow. ✅
9️⃣ Statements: Some flowers are trees. All trees are plants. No plants are stones.
Conclusions:
(I) Some flowers are plants.
(II) No trees are stones.
(III) Some flowers are not stones.
Step-by-Step Explanation
"Some flowers are trees" means there's an overlap between flowers and trees.
"All trees are plants" means trees are a subset of plants.
"No plants are stones" means plants and stones have no overlap.
(I) "Some flowers are plants" is true because if flowers overlap with trees, and trees are plants, then some flowers must be plants.
(II) "No trees are stones" is true because trees are a subset of plants, and plants have no overlap with stones.
(III) "Some flowers are not stones" is true because we've established some flowers are plants, and no plants are stones.