5.3 Syllogisms and Deductions
Key Takeaways
- A syllogism combines statements about groups and asks for a conclusion that must be true in every matching case.
- All, no, some, and only have different logical strength; changing one word can change the valid conclusion.
- Some means at least one, not most, many, or all.
- A valid deduction does not introduce a new group, reverse an only statement, or assume that overlapping groups are identical.
What a Syllogism Tests
A syllogism gives two or more statements about groups and asks what must follow. The correct answer is not the most likely workplace outcome. It is the conclusion that remains true every time the given statements are true.
Civil service exams use this skill because many job rules are written in group language. All vendors may need registration. No confidential file may be posted publicly. Some applicants may qualify for preference. The small words control the conclusion.
Quantifier Meanings
| Word or Phrase | Meaning | Safe Example |
|---|---|---|
| All A are B | Every A is inside group B | All auditors are employees |
| No A are B | A and B do not overlap | No visitors are staff members |
| Some A are B | At least one A is B | Some clerks are bilingual |
| Some A are not B | At least one A is outside B | Some forms are not complete |
| Only A are B | If something is B, it must be A | Only managers approve refunds means refund approver -> manager |
The word some is the most commonly overstated. It means at least one. It does not mean most, half, many, or all. If the statements say some permit clerks work evenings, you know that at least one permit clerk works evenings. You do not know that most permit clerks do.
Linking a Middle Term
Many syllogisms work through a shared group, often called the middle term.
Example: All grant reviewers completed ethics training. All employees who completed ethics training may access the grant portal. Therefore, all grant reviewers may access the grant portal.
The middle term is ethics training. The first statement places every grant reviewer inside the trained group. The second statement gives every trained employee portal access. Because the link covers all members at each step, the conclusion covers all grant reviewers.
When the Link Is Too Weak
Now change one word: Some grant reviewers completed ethics training. All trained employees may access the grant portal. The only forced conclusion is that some grant reviewers may access the portal.
You cannot conclude that all grant reviewers may access it. The untrained grant reviewers, if any, are not covered by the second statement. A correct answer must respect the weakest supported link.
Syllogism Trap Table
| Trap | Bad Move | Better Question |
|---|---|---|
| Reversing all | All A are B, so all B are A | Did the statement cover every B? |
| Inflating some | Some A are B, so most A are B | Does some prove more than one? |
| Creating overlap | All A are C and some B are C, so some A are B | Could A and B be different parts of C? |
| Misreading no | No A are B, so no B are A is valid, but no A are C is not | Which exact groups were separated? |
| Adding a new group | Mentions supervisors when the facts mention only clerks and trainees | Is the group in the statements? |
Concrete Examples
Valid: All sealed bids are time-stamped. No time-stamped bid may be altered after opening. Therefore, no sealed bid may be altered after opening.
Invalid: All payroll specialists are employees. Some employees work remotely. Therefore, some payroll specialists work remotely. The remote employees might be engineers, analysts, or clerks. The statements do not force overlap with payroll specialists.
Valid: Some inspectors are certified translators. No certified translator is assigned to overnight intake. Therefore, some inspectors are not assigned to overnight intake. At least one inspector is in the translator group, and that group is excluded from overnight intake.
Another useful check is to ask whether the conclusion would still be true if the unnamed members changed. Some certified translators might be clerks, analysts, or outside contractors. If the answer depends on assuming who the other members are, the conclusion is not forced.
Test-Day Method
Circle all, no, some, only, none, and at least one. Name the groups with short labels. Draw a quick containment mark for all statements, a separation mark for no statements, and an overlap mark for some statements.
Then test each answer using must be true. If you can imagine a situation where the statements are true but the answer is false, eliminate it. That imagination step is not adding outside facts; it is checking whether the conclusion is forced.
All contractor badges are temporary badges. No temporary badge allows access to the evidence room. Which conclusion must be true?
Some permit specialists are certified translators. No certified translator is assigned to overnight intake. Which conclusion must be true?
All records analysts are agency employees. All agency employees complete annual ethics training. Some records analysts process grant files. Which conclusion is guaranteed?