Statement and Conclusion

Check which conclusions logically follow

0 practice questionsPage updated 25 Sept 2026Reviewed by AISEA Editorial DeskPractice questions

Statement and Conclusion questions test whether a conclusion is logically guaranteed by the facts in a statement or group of statements. Treat the statements as true for the question, ignore outside knowledge, preserve words such as all, no and some, and accept a conclusion only when it must be true in every case allowed by the statements.

Key formulas and rules

5 rules

Valid deduction: if the premises are true, the conclusion must be true.

$P\Rightarrow Q,\;P\;\therefore\;Q$ is modus ponens.

$P\Rightarrow Q,\;\neg Q\;\therefore\;\neg P$ is modus tollens.

$A\subseteq B,\;B\subseteq C\;\Rightarrow\;A\subseteq C$ expresses a valid containment chain.

Some A are B + All B are C → Some A are C; do not create a particular fact from universal statements alone.

Key concepts

Statement, premise and conclusion

A statement supplies a fact or condition. In a multi-statement question, each given statement is a premise. A conclusion is a claim proposed after the premises. The task is not to decide whether the premise is realistic; it is to decide whether the conclusion follows from it.

Necessary truth, not possibility

A conclusion follows only if it is true in every situation that satisfies the statements. If it is true in one possible arrangement but false in another, it does not follow. This is why 'could be true' and 'must be true' are different tests.

Worked examples

Example 1

Statements: All cats are dogs. All cats are black.
Conclusions:
I. All dogs are black.
II. Some dogs are not black.
Which conclusion or conclusions follow?

Solution

Step 1: The statements place cats inside dogs and inside the black group.
Step 2: They do not say that every dog is a cat, so dogs outside the cat group may be black or not black. Conclusion I is not guaranteed.
Step 3: They also do not establish that any dog is not black. Conclusion II is not guaranteed.
Answer: Neither conclusion follows.

Example 2

Statement: India is the world's largest producer of milk.
Conclusions:
I. India is the world's largest exporter of milk.
II. India does not import milk.
Which conclusion or conclusions follow?

Solution

Step 1: The statement compares production, not exports or imports.
Step 2: Being the largest producer does not logically imply being the largest exporter.
Step 3: It also does not rule out imports.
Answer: Neither conclusion follows. Both conclusions add information that the statement does not provide.

Example 3

Statements:
1. All planners are readers.
2. All readers are careful.
3. Some planners are mentors.
Conclusion: Some mentors are careful.
Does the conclusion follow?

Solution

Step 1: From statements 1 and 2, every planner is careful.
Step 2: Statement 3 guarantees at least one person who is both a planner and a mentor.
Step 3: That person is careful through the chain.
Answer: Yes. Some mentors are careful.

Example 4

Statements:
1. If a candidate passes the screening test, the candidate is invited to interview.
2. Meera is not invited to interview.
Conclusion: Meera did not pass the screening test.
Does the conclusion follow?

Solution

Step 1: Let P mean 'passes screening' and Q mean 'is invited to interview'.
Step 2: Statement 1 gives P implies Q.
Step 3: Statement 2 gives not Q for Meera.
Step 4: Modus tollens gives not P.
Answer: Yes. Under the stated rule, Meera did not pass the screening test.

Example 5

Statements:
1. If a report is approved, it has a compliance sign-off.
2. This report has a compliance sign-off.
Conclusion: This report is approved.
Does the conclusion follow?

Solution

Step 1: The rule says approval is sufficient for a sign-off.
Step 2: The sign-off is the consequent, so its presence does not prove the antecedent.
Step 3: The report may have received a sign-off through another process or may have another status.
Answer: No. This reverses the conditional and affirms the consequent.

Example 6

Statements:
1. Some interns are analysts.
2. No intern is a manager.
Conclusion: Some analysts are not managers.
Does the conclusion follow?

Solution

Step 1: Statement 1 provides at least one person who is both an intern and an analyst.
Step 2: Statement 2 says every intern is outside the manager group.
Step 3: The analyst who is an intern is therefore not a manager.
Answer: Yes. Some analysts are not managers.

Example 7

Statements:
1. All researchers are writers.
2. No writer is careless.
Conclusion: No researcher is careless.
Does the conclusion follow?

Solution

Step 1: Every researcher is inside the writer group.
Step 2: The writer group has no careless members.
Step 3: Therefore, no researcher can be careless. This conclusion does not require proving that any researcher exists.
Answer: Yes. No researcher is careless.

Logical ConsequenceStanford Encyclopedia of Philosophy · Checked 1 Sep 2026Supports: conclusions following from premises and the necessary truth-preservation idea of logical consequence

Critical ThinkingInternet Encyclopedia of Philosophy · Checked 1 Sep 2026Supports: premises, conclusions, evidence, validity and identifying missing or assumed information

Validity and SoundnessInternet Encyclopedia of Philosophy · Checked 1 Sep 2026Supports: valid deductive forms and the distinction between validity and truth of premises

Statement and Conclusion

Key formulas and rules

Key concepts

Statement, premise and conclusion

Necessary truth, not possibility

Universal and particular words

Containment chains

Conditional reasoning

Negative conclusions and existence

Outside knowledge and wording

A reliable solving workflow

Worked examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Common mistakes and useful habits

Sources and review notes

Ready to test your understanding?

Key formulas and rules

Key concepts

Statement, premise and conclusion

Necessary truth, not possibility

Universal and particular words

Containment chains

Conditional reasoning

Negative conclusions and existence

Outside knowledge and wording

A reliable solving workflow

Worked examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Common mistakes and useful habits

Sources and review notes

Ready to test your understanding?

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