Logical Reasoning Challenges for Class 11 and 12
Logical reasoning questions ask you to decide what must follow from a set of statements. The key idea is this: a conclusion is valid only if it is true in every case that fits the statements. One counterexample is enough to reject it.
Syllogisms: testing a conclusion
A syllogism gives two statements and a conclusion. Draw the groups in your head, or sketch circles, and look for a case that makes the conclusion false.
- All A are B; all B are C. Therefore, all A are C. This is valid.
- Some A are B; no B is C. Therefore, some A are not C. This is valid, because the A that are also B cannot be C.
- All doctors are graduates; some graduates are teachers. Therefore, some doctors are teachers. This does not follow. The graduates who are teachers may contain no doctors at all.
Ordering problems
Ordering problems give comparisons, such as “P is older than Q” or “R is younger than Q”. Combine them into one chain and read off the answer. The method is to write each comparison as an arrow and follow the arrows.
Practice questions
- Statements: All cats are animals. All animals need water. Conclusion: All cats need water. Does the conclusion follow?
- Statements: No engineer is a poet. Some poets are singers. Conclusion: Some singers are not engineers. Does the conclusion follow?
- Statements: Some plants are trees. All trees are green. Conclusion: Some plants are green. Does the conclusion follow?
- Statements: A is taller than B. B is taller than C. D is shorter than C. Question: Who is the tallest?
- Statements: P is older than Q. R is younger than Q. S is older than P. Question: Who is the oldest?
Answers and explanations
1. Yes. Every cat is an animal, and every animal needs water, so every cat needs water.
2. Yes. The poets who are singers are not engineers, because no engineer is a poet. So at least some singers are not engineers.
3. Yes. The plants that are trees are green, because all trees are green. So at least some plants are green.
4. A. A is taller than B, and B is taller than C, so A is taller than both. D is shorter than C and does not change the top position.
5. S. S is older than P, and P is older than Q. R is younger than Q. So S is the oldest of the group.
Strategy for timed questions
- Read the statements once, then the conclusion. Do not try to memorise both.
- Ask: can I find a case where the statements are true and the conclusion is false?
- If you cannot find such a case, the conclusion usually follows, but check the wording of “some” and “all”.
Put your skills to the test
Play a Class 11 or Class 12 challenge on BrainSprint to practise these ideas under mixed questions. Start a challenge. For more on the number side of reasoning, read our number series guide.
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