Statements

1. Statements and their role in CSAT

A logical statement is a declarative sentence that can be evaluated as true or false within a specified context. For example, ‘Every selected candidate submitted an application’ expresses a claim. Commands, questions and wishes are not normally propositions because they do not themselves assert something true or false. An open sentence such as ‘x is greater than five’ becomes a proposition only when the value or scope of x is specified.

Statement-based reasoning appears in syllogisms, conditional reasoning, statement–conclusion questions, assumptions, arguments and analytical arrangements. A short sentence may encode a restriction that controls the whole problem. ‘Only registered applicants may enter’, for instance, establishes registration as a necessary condition for entry. It does not promise entry to every registered applicant. The examination tests careful interpretation more than familiarity with technical labels.

Three layers must be separated: the wording of the claim, its logical relationship with other claims, and its factual credibility outside the question. In a deductive problem, accept the supplied premises for the purpose of reasoning, even if they describe an imaginary situation. In a passage-based inference question, remain within the passage’s evidence and tone. Neither format authorises replacing the given information with personal experience.

• Identify the task before solving: necessarily follows, can be inferred, is assumed, strengthens, weakens or is an appropriate action.
• Underline qualifiers such as all, some, only, not, unless, most, immediately and invariably.
• Keep the same category, time period and geographical scope throughout the reasoning.

2. Quantifiers, categories and existence

Categorical statements describe relationships between classes. ‘All A are B’ places the whole A class inside B. ‘No A is B’ makes the classes disjoint. ‘Some A are B’ establishes at least one common member. ‘Some A are not B’ establishes at least one member of A outside B. Small Venn diagrams are useful because they expose relationships without requiring the solver to imagine particular people or objects.

Conversion means reversing the subject and predicate. ‘No A is B’ permits ‘No B is A’, and ‘Some A are B’ permits ‘Some B are A’. However, ‘All A are B’ does not permit ‘All B are A’. Similarly, ‘Some A are not B’ does not establish ‘Some B are not A’. These invalid reversals are common distractors because the sentence retains the same words while changing their relationship.

Existence requires particular care. Under standard modern deductive logic, ‘All unicorns are mammals’ does not establish that unicorns exist. Therefore, a universal statement alone should not be used to manufacture a ‘some’ conclusion unless existence is supplied by the question. Some coaching conventions assume existence; explicit examination instructions take precedence. Also, ‘some’ does not mean ‘some but not all’: the possibility that all members qualify remains open unless excluded.

Negation must target the exact claim. The denial of ‘All applicants qualified’ is ‘At least one applicant did not qualify’, not ‘No applicant qualified’. The denial of ‘Some applicants qualified’ is ‘No applicant qualified’. ‘Not all’ and ‘none’ are therefore very different. When interpreting most, identify the population carefully: most members of one group need not constitute most members of a larger population.

• All A are B, and all B are C, establish that all A are C.
• Some A are B, and all B are C, establish that some A are C.
• Some A are B, and some B are C, do not necessarily establish any overlap between A and C.

3. Conditional statements and valid inference

A conditional statement has the form ‘If P, then Q’. Here P is sufficient for Q, while Q is necessary for P. From ‘If a file is approved, it receives an approval number’, approval permits the inference that a number is received. Absence of that number permits the inference that the file was not approved, provided the original rule is exceptionless and applies to the file concerned.

Two valid patterns are especially important. Modus ponens moves from ‘If P, then Q’ and P to Q. Modus tollens moves from ‘If P, then Q’ and not Q to not P. The equivalent contrapositive of the conditional is ‘If not Q, then not P’. The converse, ‘If Q, then P’, and inverse, ‘If not P, then not Q’, do not automatically follow.

The errors of affirming the consequent and denying the antecedent arise when these invalid reversals are used. A file might receive a number through another procedure, so the presence of a number alone need not prove approval. Likewise, failure to obtain approval does not by itself prove the absence of a number. Translate ‘P only if Q’ as ‘If P, then Q’; translate ‘P if Q’ as ‘If Q, then P’.

Unless normally introduces an exception or necessary alternative. ‘The office will remain closed unless permission is granted’ establishes that without permission it remains closed; permission alone does not guarantee opening. A biconditional, expressed by ‘if and only if’, supports both directions. Treat ‘or’ as inclusive unless the wording excludes the possibility that both alternatives hold.

• Write long rules as short symbols, but preserve every negative.
• Chain compatible rules: if P implies Q and Q implies R, then P implies R.
• Do not turn a necessary condition into a sufficient condition.

4. Conclusions, assumptions and evidence

A necessary conclusion must survive every arrangement allowed by the premises. A possible conclusion needs only one compatible arrangement. To reject a claimed necessary conclusion, construct a counterexample in which all premises remain true but that conclusion becomes false. Failure to prove a claim does not prove its opposite: the available information may simply be insufficient.

An assumption is an unstated requirement or connecting premise of an argument. In ‘The department should digitise applications to reduce processing time’, a relevant assumption is that the proposed digitisation can reduce delays in the actual workflow. The negation test asks whether denying a proposed necessary assumption seriously undermines the reasoning. It does not require that the opposite conclusion become certain.

Strengthening and weakening questions concern the quality of support rather than deductive certainty. Evidence that addresses an alternative explanation, establishes comparability or connects cause and outcome may strengthen an argument. Evidence of reverse causation, selection bias or an omitted variable may weaken it. A fall in disease cases after a campaign is not, by timing alone, proof that the campaign caused the fall.

Argument and course-of-action questions require attention to relevance, feasibility and proportionality. An impressive statistic is weak evidence if it concerns another population or period. An action should address the identified problem and fall within the actor’s authority. Avoid extreme recommendations unsupported by the statement, such as imposing a nationwide prohibition because one local incident has been reported.

• Distinguish descriptive claims about what exists from normative claims about what ought to happen.
• Do not replace may with must, association with causation, or a sample finding with a universal claim.
• For passage-based inference, preserve the author’s qualifications and degree of confidence.

5. An efficient examination method

Begin with the question stem, then reduce the supplied information to a compact representation. Use overlapping circles for classes, arrows for conditionals and a small grid for arrangements. Resolve references such as ‘these applicants’ before testing options. For multiple conclusions, evaluate each independently rather than assuming that acceptance of one determines the status of another.

Test the strongest-looking conclusion first for an unsupported reversal, an existence claim or an enlarged scope. If it survives, try a minimal counterexample with two or three objects. For assumption questions, identify the argument’s objective and the missing connection between the evidence and recommendation. For causal questions, ask what else could explain the observed change.

Time management matters in a qualifying paper with negative marking. Solve transparent statement questions first and return to ambiguous or lengthy ones. During practice, record the reason for each error: misreading only, confusing some with all, reversing a conditional, importing external facts or overlooking an alternative explanation. Repeated error patterns are more useful for improvement than merely counting incorrect answers.

• Check whether the answer must be true, could be true or best supports the argument.
• Read every option before marking; closely related options often differ by one decisive qualifier.
• Treat the information being insufficient as a logical outcome, not as a failure to solve.

Previous year questions

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