Exercises
Challenge your logical reasoning mastery with this quiz on deductive thinking, syllogisms, conditional statements, and logical equivalence. Work through questions involving categories such as cats, mammals, birds, dogs, engineers, athletes, doctors, teachers, cars, and humans. Practice identifying what must be true, what must be false, and what can validly be concluded from a set of premises. Ideal for students and anyone looking to strengthen critical thinking, analytical reasoning, and argument-evaluation skills.
Answer the questions below and check the explanation for each answer.
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According to logical syllogism, the correct answer is that some mammals are birds. However, this doesn't logically imply that any cats, which are mammals, are birds. No cats are birds. is the logical conclusion from the given premises.
The given statement is a hypothetical and does not support contrapositive claims. Therefore, if it didn’t rain, the original premise gives no information regarding whether or not an umbrella was taken. However, If it didn’t rain, I didn’t take an umbrella. is a valid inference under classical logic.
The statement All dogs bark. implies a condition; thus, the correct equivalent statement is If it is a dog, it barks. This is a logical translation in conditional form.
The statement All engineers solve problems. does not imply that all problem solvers are engineers. The valid inference is that Some engineers may be people who solve problems.
Given the premise, any successful person must be hardworking, making Some successful people are not hardworking. logically false, as it contradicts the rule stated in the premise.
The given statements do not provide enough information to conclude that All cars are vehicles., even though it is plausible. However, the data allows to state that Some vehicles are not cars., which is certain and accurate.
Through syllogistic logic, if all A are B and all B are C, it means every A is also a C. Therefore, All A are C. is the correct deduction, as the statement possesses a transitive property.
The statement No athletes are lazy. makes it logically false for Some athletes are lazy. This contradicts the premise that separates lazy individuals from athletes.
Given that Some doctors are teachers. and No teachers are engineers., it must be true that Some doctors are not engineers., as they fall into the non-engineer teacher category.
From the logical standpoint, since John is painted as a human and all humans are declared mortals, it follows directly that John is mortal. John is mortal. is the valid conclusion.
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