5.1 Conditional Statements and If-Then Rules
Key Takeaways
- A conditional rule has a trigger and a required result; the trigger guarantees the result only in that direction.
- The contrapositive is valid: if P requires Q, then not Q proves not P when the rule is followed.
- Only, unless, required, and no are translation signals that should be rewritten before answer choices are tested.
- Most wrong answers reverse the rule, add a likely but unstated reason, or turn a possible conclusion into a required one.
Why Conditional Logic Matters
Civil service basic skills tests often include logical reasoning, and OpenExamPrep's balanced blueprint assigns Logical Reasoning 20% of the practice mix. Your actual hiring notice may combine logic with reading, judgment, clerical checking, or a job-specific assessment.
Conditional logic matters because government work is rule driven. A clerk may need to know when a form must be returned, when a record must be restricted, or when a case must be escalated. The exam is checking whether you follow the written rule, not whether you can imagine what usually happens in an office.
The Basic If-Then Shape
A conditional statement has two parts: the trigger and the required result. Write it as If P, then Q. The P side is enough to force Q. The Q side, by itself, does not prove P.
Example: If a complaint alleges a safety hazard, the complaint must be sent to the safety officer. A safety-hazard complaint must be sent there. But a complaint sent to the safety officer might have been sent for another reason, such as a workplace injury or building-code issue.
| Rule Wording | Clean Translation | What Is Safe |
|---|---|---|
| If the form is unsigned, return it | unsigned -> return | An unsigned form must be returned |
| Only cleared staff may enter Room 4 | enter Room 4 -> cleared | Anyone who entered Room 4 is cleared |
| A permit is required for a street closure | street closure -> permit | No permit means no valid street closure |
| Unless identification is shown, no badge is issued | no ID -> no badge | Badge issued means ID was shown |
| No late application is accepted without a waiver | late and accepted -> waiver | A late accepted application had a waiver |
Direct Rule and Contrapositive
Use two moves before you consider anything else. The direct rule says that if P happened, Q must happen. The contrapositive says that if Q did not happen, P did not happen.
Rule: If a record contains medical information, it must be marked confidential. If the record contains medical information, mark it confidential. If the record is not marked confidential, it cannot contain medical information, assuming the rule was followed.
The contrapositive often feels backward, but it is reliable. It works because the rule made Q required every time P appears. If Q is missing, the trigger could not have appeared under a properly followed rule.
Translation Signals
Some conditional rules avoid the word if. On the exam, rewrite them before reading answer choices.
| Signal Word | How to Read It | Example |
|---|---|---|
| only | The phrase after only is required | Only supervisors approve refunds: refund approved -> supervisor |
| unless | Treat as if not | Unless ID is shown, no entry: no ID -> no entry |
| required | The requirement is the result | A signature is required for filing: filed -> signature |
| no or none | The groups cannot overlap | No expired license is valid: expired -> not valid |
| all or every | Each item in the first group is in the second | All sealed bids are logged: sealed bid -> logged |
Trap Table
| Trap | What the Wrong Answer Does | Quick Check |
|---|---|---|
| Reversing the rule | Treats Q as proof of P | Ask whether another reason for Q is possible |
| Denying the trigger | Says not P means not Q | Ask whether Q could happen for a different trigger |
| Adding a cause | Supplies a real-world explanation not stated | Use only the rule and given fact |
| Overusing must | Changes may, can, or possible into required | Match the strength of the rule |
| Misreading only | Puts the arrow in the wrong direction | Put the required condition on the right side |
Concrete Walkthrough
Rule: If an expense claim is missing a receipt, payroll must hold the claim for review. Fact: Payroll did not hold Claim 17 for review. Valid conclusion: Claim 17 was not missing a receipt.
Do not conclude that Claim 17 was approved, paid, complete, or submitted on time. Those facts might be true, but the rule did not say them. A civil service logic item rewards the narrow conclusion that is forced by the condition.
Timed Method
Underline the trigger words first: if, only, unless, all, no, required. Rewrite the rule with a short arrow. Mark the given fact as matching the left side, right side, or negation of one side.
Then test answer choices against the arrow. If the answer reverses direction, adds a reason, or uses a stronger word than the rule supports, eliminate it. This small setup usually takes less time than rereading a confusing sentence three times.
Rule: If a complaint includes an immediate safety hazard, it must be logged before it is referred to another unit. Complaint M was referred before any log entry was created. Assuming the rule was followed, what must be true?
Rule: A visitor badge may be issued only if the visitor presents identification and signs the visitor register. A visitor received a badge. What follows?
Rule: Unless a fee waiver is approved, late applications are not accepted. A late application was accepted. Which conclusion is required?