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Brain’s QuotientSTAY CURIOUS.

Think it through: methods, examples, and logical reasoning practice

Published: 23 February, 2023 — Updated 6 September 2026 by Brain's Quotient

A yellow tile completing a connected sequence of blue tiles

Six sets, with a method for each

Start with the basic sets, then apply the same ideas to linked clues. Treat every stated rule as true and use only the information given. Read an example, explain its reasoning in your own words, and then try unfamiliar questions.

Set 1: Logical deductions

Draw nested groups for 'all' and a shared region for 'some'. Use only overlaps the clues actually guarantee.

Worked example: All owls in a park are birds. No birds there are indoors. An owl in that park cannot be indoors: follow owl → bird → not indoors.

Common mistake: 'Some' does not mean 'all', and two groups sharing a larger group do not necessarily overlap each other.

Set 2: Ordering and comparison

Write one ordered chain. Combine clues through a shared person or object. Leave unrelated pairs undecided.

Worked example: R is before S, and T is before R. Combining the clues gives T → R → S. R must be second among these three.

Common mistake: 'Before' does not mean 'immediately before'. Two people both ahead of someone are not ordered relative to each other.

Set 3: Conditions and rules

Read 'if A, then B' as a one-way arrow. A guarantees B; missing B rules out A.

Worked example: If a badge is gold, it opens a door. A badge that does not open that door cannot be gold, assuming the rule holds.

Common mistake: An open door does not prove a gold badge was used. A rule can describe one sufficient cause without listing all causes.

Set 4: Linked deductions

Follow a known member through each group rule. To test whether a conclusion must hold, try constructing a case where it fails.

Worked example: All kites in a collection are toys. Some toys are red. The red toys could all be balls, so a red kite is not guaranteed.

Common mistake: A possible conclusion is weaker than a necessary one. Universal rules alone do not establish that a group has any members.

Set 5: Ordering with constraints

Number the positions, place fixed items, then treat adjacent items as a block. Test each remaining arrangement against every clue.

Worked example: Four tiles J, K, L, M fill a row. M is first and J-K are adjacent in that order. M-J-K-L and M-L-J-K both work: adjacency alone does not fix a position.

Common mistake: Finding one valid arrangement proves it is possible, not that it is the only one. Look for a second arrangement before saying 'must'.

Set 6: Testing conditions

Try to break the rule: find a case where its condition holds but its consequence fails. For a chain, follow each link before drawing a conclusion.

Worked example: To test 'every square token is blue', look for a square token that is not blue. A blue circle does not disprove the rule.

Common mistake: 'Only if' introduces a necessary condition. 'If and only if' gives both directions. Keep 'at least one' separate from 'exactly one'.

After a mistake, identify the clue you misread or the assumption you added. Retry it, then move to another set: a higher retry score may reflect remembering answers. Your practice score describes this attempt, not your IQ or general improvement.

Choose a free practice set

Explore the background and more examples below.

What is Logical Reasoning?

Logical reasoning is a critical thinking skill that involves the ability to analyze and evaluate arguments and evidence to reach a conclusion. It is an essential skill for problem-solving, decision-making, and effective communication.

Logical reasoning is an essential skill that can help you make better decisions, solve complex problems, and communicate effectively. It involves the ability to evaluate evidence and arguments to reach a conclusion. Logical reasoning is used in many fields, including science, law, business, and everyday life.

There are different types of logical reasoning, including deductive and inductive reasoning. Deductive reasoning involves starting with a general principle and using it to draw specific conclusions. Inductive reasoning, on the other hand, involves using specific observations or evidence to draw a general conclusion. Both types of reasoning are important and useful in different contexts.

Overview of Logical Reasoning

Logical reasoning is a process of using evidence, premises, and principles to reach a conclusion. It involves evaluating arguments and evidence to determine their validity and soundness. A valid argument is one where the conclusion logically follows from the premises, while a sound argument is one where the premises are true.

Logical reasoning involves the following steps:

  1. Identifying the premises

    The premises are the statements or evidence used to support the argument.

  2. Identifying the conclusion

    The conclusion is the statement that follows from the premises.

  3. Evaluating the argument

    This involves determining whether the premises support the conclusion and whether the argument is valid and sound.

Types of Logical Reasoning

There are different types of logical reasoning, including deductive and inductive reasoning. Each type of reasoning is used in different contexts.

Deductive Reasoning

Deductive reasoning involves starting with a general principle and using it to draw specific conclusions. It is often used in mathematics, logic, and philosophy. Deductive reasoning is based on the idea that if the premises are true, the conclusion must also be true. An example of deductive reasoning is:

  • Premise 1: All mammals have lungs.
  • Premise 2: A dog is a mammal.
  • Conclusion: Therefore, a dog has lungs.

In this example, the conclusion follows logically from the premises, making the argument valid and sound.

Inductive Reasoning

Inductive reasoning involves using specific observations or evidence to draw a general conclusion. It is often used in science and social sciences. Inductive reasoning is based on the idea that if the premises are true, the conclusion is likely to be true. An example of inductive reasoning is:

  • Premise 1: Every crow we have seen is black.
  • Conclusion: Therefore, all crows are black.

In this example, the conclusion is not necessarily true, but it is likely to be true based on the evidence. Inductive reasoning is used to develop theories and hypotheses in scientific research.

Tips for Improving Logical Reasoning

Improving your logical reasoning skills can help you make better decisions and communicate more effectively. Here are some tips to help you improve your logical reasoning skills:

  1. Practice identifying premises and conclusions

    Start by identifying the premises and conclusions in arguments you encounter in your daily life. This will help you develop your ability to recognize arguments and evaluate their validity.

  2. Practice evaluating arguments

    Once you have identified the premises and conclusions, practice evaluating the arguments to determine their validity and soundness. Ask yourself if the premises support the conclusion and if the argument is valid and sound. This will help you develop your critical thinking skills and improve your ability to make well-reasoned decisions.

  3. Practice using deductive and inductive reasoning

    Use deductive reasoning to draw specific conclusions from general principles and inductive reasoning to draw general conclusions from specific observations or evidence. This will help you understand the different types of reasoning and when to use them.

  4. Learn to recognize logical fallacies

    Logical fallacies are errors in reasoning that can make arguments invalid or unsound. Common logical fallacies include ad hominem attacks, straw man arguments, and false dichotomies. Learning to recognize logical fallacies can help you avoid making them and improve the quality of your arguments.

  5. Use examples to illustrate your points

    Using examples can help make your arguments more persuasive and easier to understand. When making an argument, try to provide specific examples to support your points.

Logical Reasoning Practice Exercises

Here are some practice exercises to help you improve your logical reasoning skills:

  1. Identify the premises and conclusion in the following argument:
    • Premise 1: All cats are mammals.
    • Premise 2: All mammals have fur.
    • Conclusion: Therefore, all cats have fur.
  2. Evaluate the following argument for validity and soundness:
    • Premise 1: All dogs have four legs.
    • Premise 2: Fido is a dog.
    • Conclusion: Therefore, Fido has four legs.
  3. Use deductive reasoning to draw a conclusion from the following premise:
    • Premise: All birds have wings
    • Conclusion: All birds have wings, and therefore, anything that does not have wings cannot be classified as a bird.
  4. Use inductive reasoning to draw a conclusion from the following premise:
    • Premise: Every time I eat peanuts, I get a headache.
    • Conclusion: Eating peanuts causes headaches for the person making the claim.

Common Logical Fallacies

Here are some common logical fallacies to avoid when making arguments:

  1. Ad hominem: Attacking the person making the argument rather than addressing the argument itself.
    • Person A: I think we should invest in renewable energy.
    • Person B: That's a terrible idea. You probably just want to destroy the economy.

    Person B implies that Person A's suggestion is a bad idea because they want to "destroy the economy," without providing any evidence or reasoning to support this claim. Person B is attacking Person A rather than addressing the merits of their proposal.

  2. Straw man: Misrepresenting an opponent's argument in order to make it easier to attack.
    • Person A: I think we should prioritize funding for education in our state budget.
    • Person B: I can't believe you want to throw all our money at schools. Don't you care about anything else? What about public safety, healthcare, and infrastructure?

    Person A never said that they want to allocate all of the state's money to education, but Person B misrepresents their argument as an extreme position. By creating a "straw man" argument that is easy to attack, Person B avoids engaging with the real issue at hand, which is whether or not education should be a priority in the state budget.

By avoiding these and other logical fallacies, you can strengthen your arguments and make them more persuasive and effective.

Online Logical Reasoning Practices and Services

There are several online Logical Reasoning Practices and Services available, but it's important to keep in mind that online tests may not be as accurate or reliable as those administered by a trained professional. That being said, here are a few Logical Reasoning Practice services you could consider:

  • AssessmentDay

    AssessmentDay offers practice aptitude tests and assessment advice to help job-seekers prepare for employment selection tests.

  • Brain's Quotient

    Brain's Quotient offers six free sets of ten logical reasoning questions with no timer. Learn mode explains each answer as you go; Challenge mode saves explanations until the end. Results show correct answers and percentage accuracy, not an IQ estimate.

  • Lumosity

    Lumosity offers brain training games that help improve your cognitive abilities, including logic and reasoning.

Conclusion

Logical reasoning is an essential skill for problem-solving, decision-making, and effective communication. By understanding the different types of reasoning and practicing your skills, you can improve your ability to evaluate arguments and evidence and make well-reasoned decisions. Remember to practice identifying premises and conclusions, evaluating arguments, using deductive and inductive reasoning, learning to recognize logical fallacies, and using examples to illustrate your points. With these skills, you can become a more effective and persuasive communicator and decision-maker.

Summary

  • Logical reasoning is an important skill for problem-solving, decision-making, and effective communication.
  • There are different types of reasoning, including deductive and inductive reasoning, and it's important to understand when to use them.
  • Practice exercises, such as identifying premises and conclusions and evaluating arguments for validity and soundness, can help improve logical reasoning skills.
  • It's also important to learn to recognize logical fallacies and use examples to support arguments.
  • Online Logical Reasoning Practices and Services: AssessmentDay, Brain's Quotient, and Lumosity

References