Free Logical Deductions MCQs with Answers

1. All pens are pencils. All pencils are erasers. Which conclusion follows?

• A. All erasers are pens
• B. All pens are erasers
• C. Some erasers are not pencils
• D. No pen is an eraser

Explanation: The two statements chain together, so everything in the pen category is inside pencils and therefore inside erasers. Reversing the chain to say all erasers are pens is invalid, since the outer category may contain much more. Drawing three nested circles settles the question immediately.

2. Some books are novels. All novels are stories. Which conclusion follows?

• A. All books are stories
• B. Some books are stories
• C. No book is a story
• D. All stories are books

Explanation: The books that are novels must also be stories, which guarantees that at least some books are stories, but nothing is known about the remaining books. A conclusion beginning with all cannot follow from a premise beginning with some. The reversal in the last option is invalid for the same reason.

3. No teacher is lazy. Some employees are teachers. Which conclusion follows?

• A. All employees are lazy
• B. Some employees are not lazy
• C. No employee is lazy
• D. Some teachers are employees only

Explanation: The employees who are teachers cannot be lazy, so at least some employees are not lazy, but the rest are unaccounted for. Concluding that no employee is lazy goes far beyond the premises. The valid conclusion is always the weakest one the premises actually support.

4. If it rains, the match is cancelled. The match was not cancelled. Which conclusion follows?

• A. It rained
• B. It did not rain
• C. The match was postponed
• D. Nothing can be concluded

Explanation: Denying the consequence of a conditional lets you deny its antecedent, which is the valid form known as modus tollens. Had the match been cancelled, nothing would follow, since it might have been cancelled for another reason. Recognising which direction is valid is the whole point of these questions.

5. If a student passes the entry test, they can join the college. Sana joined the college. Which conclusion follows?

• A. Sana passed the entry test
• B. Sana did not pass the entry test
• C. Sana may or may not have passed the entry test
• D. The entry test was easy

Explanation: The statement says passing is sufficient for joining, not that it is the only route, so Sana might have joined through a quota, transfer or other channel. Concluding that she passed would be affirming the consequent, an invalid form. Watch carefully for the difference between sufficient and necessary conditions.

6. All squares are rectangles. Some rectangles are not squares. Which statement must be true?

• A. Squares are a subset of rectangles
• B. Rectangles are a subset of squares
• C. No rectangle is a square
• D. All rectangles are squares

Explanation: The first premise places squares entirely inside rectangles and the second confirms that rectangles extend beyond squares, so the relationship is one of proper subset. The remaining options either reverse the containment or deny the overlap that the first premise establishes. Subset language is simply a precise way of stating all A are B.

7. Statements: All cats are animals. Some animals are wild. Which conclusion follows?

• A. Some cats are wild
• B. All cats are wild
• C. No definite conclusion about cats being wild can be drawn
• D. No cat is wild

Explanation: The wild animals mentioned might be entirely outside the cat group, so nothing definite follows about cats either way. A middle term used with some in one premise cannot carry a firm conclusion. Being unable to conclude is itself the correct answer in many syllogism questions.

8. Only members can use the library. Bilal is using the library. Which conclusion follows?

• A. Bilal is a member
• B. Bilal is not a member
• C. Bilal is a student
• D. Nothing follows

Explanation: The word only makes membership a necessary condition for use, so anyone using the library must be a member. This is the reverse of the usual if then structure, which is why only sentences must be read carefully. Being a member, however, would not guarantee that he uses it.

9. If A is taller than B, and B is taller than C, then

• A. C is taller than A
• B. A is taller than C
• C. A and C are of equal height
• D. Nothing can be said

Explanation: Height comparisons are transitive, so the relationship carries through the chain from A to C. Not all relationships behave this way: being a friend of, for example, is not transitive. Checking whether a relation is transitive before chaining it is a useful habit.

10. In a queue, Ali is 7th from the front and 12th from the back. How many people are in the queue?

• A. 18
• B. 19
• C. 20
• D. 17

Explanation: Adding the two positions counts Ali twice, so the total is 7 plus 12 minus 1, which is 18. Forgetting to subtract the one is the standard error and gives 19. The same formula applies to any single object counted from both ends.