Logical Reasoning · Statements & Arguments
Logical Deduction — Questions & Answers
Logical deduction questions (syllogisms) give statements such as "All A are B" and ask which conclusions follow. Drawing the sets as circles shows exactly what must be true.
- 5 solved questions
- Step-by-step AI walkthroughs
- How-to-approach tips
How to approach
Treat the statements as true, however odd they sound. Draw a quick Venn diagram and test each conclusion: it follows only if it is true in every possible diagram. If neither follows but the two are opposites (some / none, all / some-not), exactly one must be true, so choose "Either".
Chain the statements one link at a time. Only a conclusion true in every diagram counts; a conclusion that is merely possible does not.
An option can be true unless it contradicts the statements. Look for the one that clashes with what is definitely true.
Find the second statement that joins the first to the conclusion. Test each option: with it added, is the conclusion true in every diagram?
5 solved Logical Deduction questions
Statements: All trains are rivers. All rivers are ropes.
Conclusions:
I. All trains are ropes.
II. Some ropes are rivers.
Which of the conclusions logically follow?Solution — answer E
Both. Trains are inside rivers, which are inside ropes, so all trains are ropes (I); every river is a rope, so some ropes are rivers (II).
4 steps · reveal one at a timeStep 1: Analyze Statements
Let's break down the given statements. "All trains are rivers" means the set of trains is entirely contained within the set of rivers. "All rivers are ropes" means the set of rivers is entirely contained within the set of ropes.
Step 2: Evaluate Conclusion I
Consider Conclusion I: "All trains are ropes." Since all trains are rivers, and all rivers are ropes, it logically follows that all trains must also be ropes. Think of it as a chain: Trains ⊂ Rivers ⊂ Ropes. This conclusion is valid.
Step 3: Evaluate Conclusion II
Now let's look at Conclusion II: "Some ropes are rivers." If all rivers are ropes, it means that the set of rivers is a part of the set of ropes. Therefore, there must be at least some ropes that are also rivers. This conclusion is also valid.
Step 4: The answer
So the answer is (E) I and II are both valid conclusions. Both conclusions logically follow from the given statements.
Statements: All carts are wheels. Some wheels are tyres. No tyres are rails.
Which conclusion definitely follows from the statements?Solution — answer C
The wheels that are tyres can't be rails, so some wheels are not rails. Carts need not touch the tyres, so nothing definite follows about carts.
4 steps · reveal one at a timeStep 1: Understand statements
Let's break down the given statements. We know that all carts are wheels. Also, some wheels are tyres, meaning there's an overlap. Finally, no tyres are rails, so tyres and rails are completely separate.
Step 2: Connect key facts
We have "Some wheels are tyres" and "No tyres are rails". This tells us that the specific group of wheels that are also tyres cannot be rails. They are mutually exclusive categories.
Step 3: Form a conclusion
Since there are wheels that are tyres, and none of these tyres can be rails, it logically follows that these particular wheels cannot be rails either. Therefore, some wheels are not rails.
Step 4: The answer
So the answer is (C) Some wheels are not rails. The wheels that are tyres cannot be rails, which means some wheels are definitely not rails.
Statements: All poets are singers. No singers are painters.
If the statements are true, which of these CANNOT be true?Solution — answer B
Poets are inside singers, and singers and painters don't overlap, so "some poets are painters" can never be true. The others are possible (some are certain).
5 steps · reveal one at a timeStep 1: Understand the first statement
The first statement, "All poets are singers," means that the group of poets is entirely contained within the group of singers. If someone is a poet, they must also be a singer.
Step 2: Understand the second statement
The second statement, "No singers are painters," tells us that the group of singers and the group of painters have absolutely no members in common. They are completely separate categories.
Step 3: Combine the statements
Since all poets are singers, and no singers are painters, it logically follows that no poets can be painters. If poets are inside the singers' group, and singers don't overlap with painters, then poets also cannot overlap with painters.
Step 4: Evaluate the options
We're looking for what CANNOT be true. Our combined understanding is that no poets are painters. Therefore, any statement suggesting that some poets are painters must be false, and thus cannot be true.
Step 5: The answer
So the answer is (B) Some poets are painters. This statement directly contradicts our deduction that no poets can be painters, making it impossible for it to be true.
Statement: All bulbs are lights.
Conclusion: All bulbs are fixtures.
Which second statement would make the conclusion follow?Solution — answer C
All lights are fixtures completes the chain: bulbs are inside lights, lights inside fixtures. Any other option leaves some bulbs possibly outside the fixtures.
4 steps · reveal one at a timeStep 1: Understand the Goal
We are given the statement: All bulbs are lights. Our goal is to make the conclusion All bulbs are fixtures follow logically. We need a second statement to connect 'lights' to 'fixtures'.
Step 2: Identify the Missing Link
If all bulbs are lights, and we want all bulbs to be fixtures, then the group of 'lights' must be entirely contained within the group of 'fixtures'. If any light isn't a fixture, then a bulb (which is a light) might not be a fixture.
Step 3: Formulate the Rule
To ensure every bulb is a fixture, the second statement must establish that all items classified as 'lights' are also classified as 'fixtures'. This creates a chain: bulbs ⊂ lights ⊂ fixtures.
Step 4: The answer
So the answer is (C) All lights are fixtures. This statement completes the logical chain, ensuring that if all bulbs are lights, and all lights are fixtures, then all bulbs must necessarily be fixtures.
Statements: All candles are rockets. Some rockets are fans.
Conclusions:
I. Some candles are fans.
II. No candles are fans.
Which of the conclusions logically follow?Solution — answer C
Either. Neither follows alone, since the fan-rockets may or may not include candles. But I and II are opposites (some / none), so exactly one of them is true.
5 steps · reveal one at a timeStep 1: Analyze the Statements
We have two statements. "All candles are rockets" means every candle is also a rocket. "Some rockets are fans" means there's at least one rocket that is also a fan, but not necessarily all rockets.
Step 2: Evaluate Conclusion I
Conclusion I states: "Some candles are fans." From the statements, we know some rockets are fans. However, these fan-rockets might or might not include candles. We cannot definitively say that some candles are fans. So, I is not necessarily true.
Step 3: Evaluate Conclusion II
Conclusion II states: "No candles are fans." Similar to Conclusion I, the rockets that are fans could potentially include candles, or they might not. We cannot definitively say that no candles are fans. So, II is not necessarily true.
Step 4: Consider Both Conclusions
Neither conclusion I nor II can be proven true from the statements alone. However, notice that "Some candles are fans" and "No candles are fans" are contradictory opposites. If one is true, the other must be false, and vice versa. Exactly one of them must be true.
Step 5: The answer
So the answer is (C) Either I or II is a valid conclusion. Since I and II are direct opposites, one of them must logically follow, even if we can't determine which one from the given information.
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