Reasoning — Statement and Conclusion

From (1) "All pens are pencils" and (2) "All pencils are erasers", it logically follows that "All pens are erasers". So, conclusion I follows. If "All pens are erasers", then "Some erasers are pens" is also a definite conclusion (as the set of pens is a subset of erasers). So, conclusion II follows. Therefore, both conclusions I and II follow.

Statement 1 says the company will provide free training on new software. Statement 2 says many employees are not familiar with it. Conclusion I: "The company wants to improve the skills of its employees." This is a direct logical inference. Providing training is a way to improve skills. So, I follows. Conclusion II: "Employees will be able to use the new software after training." While this is the *goal* of training, the statements do not guarantee its *success*. It's an assumption that all employees *will be able* to use it, not a definite conclusion. So, II does not follow. Therefore, only conclusion I follows.

Statements: "Some books are pens" and "Some pens are pencils". We cannot establish a definite direct relationship between "books" and "pencils". Conclusion I: "Some books are pencils." This is possible but not definite. Conclusion II: "No book is a pencil." This is also possible but not definite. However, conclusions I and II form a complementary pair (Some A are B vs. No A are B). They involve the same two elements (books, pencils). Since both are individually uncertain but together cover all possibilities for the relationship between books and pencils, either one or the other must be true. Therefore, either conclusion I or conclusion II follows.

Statement 1: "All students in this class are intelligent." (Class -> Intelligent) Statement 2: "Rahul is not intelligent." (Not Intelligent -> Not Class) Conclusion I: "Rahul is not in this class." This directly follows from the contrapositive of statement 1. If all students in the class are intelligent, and Rahul is not intelligent, then Rahul cannot be a student in this class. So, I follows. Conclusion II: "Rahul should study harder." This is a prescriptive statement, an advice, or an opinion. It cannot be logically concluded from the given factual statements. So, II does not follow. Therefore, only conclusion I follows.

Statement 1: "No car is a truck." (Car and Truck are disjoint sets) Statement 2: "All trucks are buses." (Trucks are a subset of Buses) Conclusion I: "No car is a bus." This does not necessarily follow. While no car is a truck, some cars *could* be buses, as the set of buses is larger than just trucks. For example, a car could be a bus, as long as it's not a truck. So, I does not follow. Conclusion II: "Some buses are trucks." Since "All trucks are buses", it means the set of trucks is entirely contained within the set of buses. Therefore, some part of buses must be trucks. This is a definite conclusion. So, II follows. Therefore, only conclusion II follows.

Statement 1: Government increases petrol tax by 10%. Statement 2: Petrol price stable for 3 months. Conclusion I: "People will reduce their petrol consumption." This is an assumption about consumer behavior, not a definite conclusion. While an increase in price *might* lead to reduced consumption, it's not guaranteed (e.g., if demand is inelastic or people have no alternatives). So, I does not follow. Conclusion II: "The government aims to increase its revenue." Increasing tax is a direct method for a government to increase its revenue. This is a logical and primary objective behind such a decision. So, II follows. Therefore, only conclusion II follows.

Statement 1: "Some birds are animals." (There's an overlap between Birds and Animals) Statement 2: "No animal is a plant." (Animals and Plants are disjoint sets) From these, we know that the "some birds" that are animals cannot be plants. Conclusion I: "Some birds are not plants." Since there are some birds that are animals, and no animal is a plant, those specific birds (which are animals) cannot be plants. This is a definite conclusion. So, I follows. Conclusion II: "No bird is a plant." This is not necessarily true. While the birds that are animals are not plants, there could be other birds (that are not animals) which *could* be plants (though biologically incorrect, we stick to logic). Or, more simply, we only know *some* birds are not plants, we cannot conclude *no* bird is a plant. So, II does not follow. Therefore, only conclusion I follows.

Statement 1: "If Hardworking (H), then Succeed (S)." (H -> S) Statement 2: "Rohit succeeded." (Rohit is S) Conclusion I: "Rohit is a hardworking person." (Rohit is H) From H -> S, we cannot conclude S -> H. This is a fallacy of affirming the consequent. There might be other ways to succeed apart from being hardworking. So, I does not follow. Conclusion II: "Success is only for hardworking people." This means "If Succeed (S), then Hardworking (H)" or "Only H succeed". This is equivalent to S -> H, which is not stated. The statement says "If H, then S", not "If S, then H". So, II does not follow. Therefore, neither conclusion I nor conclusion II follows.

Statement 1: Government bans plastic bags. Statement 2: Plastic bags cause pollution. Conclusion I: "The government is concerned about environmental protection." Since plastic bags are a major cause of pollution, and the government is banning them, it is a logical inference that the government is concerned about the environment. So, I follows. Conclusion II: "People will stop using plastic bags after the ban." While the ban is intended to stop usage, it does not guarantee that people *will* stop. There might be illegal sales, or people might use alternatives. This is an assumption about the effectiveness of the ban and public compliance, not a definite conclusion. So, II does not follow. Therefore, only conclusion I follows.

Statement 1: All Fruits (F) are Sweet (S). (F ⊆ S) Statement 2: Some Sweets (S) are Healthy (H). (S ∩ H ≠ Ø) Statement 3: No Healthy (H) food is Junk Food (J). (H ∩ J = Ø) Conclusion I: "Some fruits are healthy." From F ⊆ S and S ∩ H ≠ Ø, we know some sweets are healthy. But we don't know if those healthy sweets are also fruits. It's possible that the healthy sweets are only the non-fruit sweets. So, we cannot definitely conclude that some fruits are healthy. I does not follow. Conclusion II: "Some sweets are not junk food." From statement 2, "Some sweets are healthy." (S ∩ H ≠ Ø) From statement 3, "No healthy food is junk food." (H ∩ J = Ø) This means that the "some sweets" that are healthy cannot be junk food. Therefore, "Some sweets are not junk food" is a definite conclusion. So, II follows. Therefore, only conclusion II follows.