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Logical reasoning is a critical skill tested in many competitive exams. One of the foundational topics in this area is understanding statements and conclusions. In reasoning tests, you are often given one or more statements and asked to decide which conclusions logically follow from them.
But what exactly are statements and conclusions? Why is it important to distinguish between them? A statement is a sentence that declares a fact or an assertion that can be either true or false. A conclusion, on the other hand, is a logical deduction or inference drawn from one or more statements.
Mastering this topic helps you sharpen your critical thinking, avoid assumptions, and make precise judgments - all essential for success in aptitude tests and real-life decision-making.
A statement is a declarative sentence that expresses a fact or an assertion which can be classified as either true or false. It must be clear and unambiguous.
It is important to differentiate statements from other types of sentences such as questions, commands, or exclamations, which do not have a truth value and therefore are not statements.
| Sentence | Type | Truth Value | Explanation |
|---|---|---|---|
| The Earth revolves around the Sun. | Statement | True | Declares a fact that can be verified. |
| Is it raining outside? | Question | Not applicable | Asks for information, no truth value. |
| Close the door. | Command | Not applicable | Gives an instruction, no truth value. |
| Wow! What a beautiful painting. | Exclamation | Not applicable | Expresses emotion, no truth value. |
| Some birds can fly. | Statement | True | Declarative sentence with truth value. |
A conclusion is a logical judgment or inference drawn from one or more statements. It is what you deduce based on the information provided by the statements.
For a conclusion to be valid, it must logically follow from the given statements without introducing any new assumptions or information.
For example, if the statement is "All fruits have seeds," a valid conclusion could be "An apple has seeds," because it logically follows. However, concluding "All apples are sweet" would be invalid unless the statement explicitly supports it.
To decide whether a conclusion is valid, follow a systematic approach. This helps avoid errors and ensures logical consistency.
graph TD A[Read the Statements Carefully] --> B[Identify the Facts Given] B --> C[Analyze the Conclusion] C --> D{Does the Conclusion Follow Logically?} D -- Yes --> E[Conclusion is Valid] D -- No --> F[Conclusion is Invalid]Stepwise process explained:
Statement: All cars have four wheels.
Conclusion: A vehicle with four wheels is a car.
Is the conclusion valid?
Step 1: The statement says all cars have four wheels. This means every car has four wheels, but it does not say that only cars have four wheels.
Step 2: The conclusion claims that any vehicle with four wheels is a car. This is not supported by the statement because other vehicles (like trucks, buses) also have four wheels.
Answer: The conclusion is invalid because it does not logically follow from the statement.
Statements:
Conclusion: Whales are warm-blooded.
Is the conclusion valid?
Step 1: From the first statement, all mammals are warm-blooded.
Step 2: The second statement says whales are mammals.
Step 3: Combining these, whales must be warm-blooded because they belong to the group of mammals.
Answer: The conclusion is valid.
Statement: Some students in the class play football.
Conclusion: All students in the class play football.
Is the conclusion valid?
Step 1: The statement says some students play football, which means at least one or more, but not necessarily all.
Step 2: The conclusion claims all students play football, which is a much stronger statement.
Step 3: Since the statement does not support the conclusion fully, it introduces an assumption that is not given.
Answer: The conclusion is invalid.
Statements:
Conclusion: Some doctors are professionals.
Is the conclusion valid?
Step 1: From the first statement, all doctors are educated.
Step 2: Some educated people are teachers, but this does not mean all educated people are teachers.
Step 3: All teachers are professionals, so the group of teachers is a subset of professionals.
Step 4: The conclusion says some doctors are professionals. But doctors are educated, and only some educated people are teachers (who are professionals). There is no direct link that doctors are teachers or professionals.
Answer: The conclusion is invalid because it assumes doctors are part of the subset of teachers/professionals without evidence.
Statement: No student who studies hard fails the exam.
Conclusion 1: All students who fail the exam do not study hard.
Conclusion 2: Some students who study hard pass the exam.
Which conclusions are valid?
Step 1: The statement says "No student who studies hard fails," meaning studying hard guarantees passing.
Step 2: Conclusion 1 says "All students who fail do not study hard," which is the contrapositive of the statement and logically valid.
Step 3: Conclusion 2 says "Some students who study hard pass," which is also valid because if none failed, some must have passed.
Answer: Both conclusions are valid.
When to use: At the start of every statement and conclusion question.
When to use: When conclusions seem plausible but may rely on assumptions.
When to use: When evaluating conclusions with strong qualifiers.
When to use: During timed competitive exams.
When to use: When statements are complex or lengthy.
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