5.3 Syllogisms and Verbal Logic

What a syllogism is on this battery

A syllogism gives you two (sometimes three) premises and a conclusion, then asks whether the conclusion must be true, could be true, or cannot be true. The nouns may be firefighters, BA operators, pumpers, and exposures so the screen feels occupational. The logic does not care. If the premises do not say that every officer is a firefighter, you may not import Queensland rank structure to "help." Extra-world knowledge is not a hidden premise.

This skill sits in Core Abilities literacy and reasoning, not in a third official reading paper. The current pack names Mechanical Reasoning and Core Abilities. QFD does not publish how many syllogism items you will see, how they are weighted, or a percentage pass mark. Independent OpenExamPrep items below train the pictures. They are not official QFD questions.

Pearson VUE / OnVUE rules still ban pens and paper. You cannot draw a tidy Venn diagram on the desk. You can still hold two circles in your head: where they must overlap, where they may overlap, and where they must not.

All, some, and none

All A are B (every, each) means circle A sits inside circle B. Every BA operator in the stem's universe is a firefighter. There may still be firefighters who are not BA operators. That leftover region is allowed unless a second premise closes it.

No A are B (none, not any) means the circles do not overlap. No defensive crew is making an interior attack. If Crew 3 is making an interior attack, Crew 3 is not a defensive crew. That is a valid chain.

Some A are B (at least one) means the circles overlap in at least one individual. It does not tell you about the rest of A or the rest of B. Some officers are BA operators. Other officers may not be. Other BA operators may not be officers.

Some A are not B means A has a region outside B. Some appliances are not pumpers. That is enough to kill "all appliances are pumpers." It is not enough to prove "no appliances are pumpers."

Most is not all and is stronger than a bare some. If an item uses most, do not upgrade it to all, and do not downgrade it to "maybe none." Aptitude stems more often stay with all / some / none. Use the word that is on the screen.

Must-be-true versus could-be-true

Must be true appears in every Euler picture that still respects the premises. Could be true appears in at least one legal picture and fails in another. Cannot be true contradicts a premise in every picture.

Worked must-be-true. Premise 1: All BA operators at this incident are firefighters. Premise 2: Some officers at this incident are BA operators. Conclusion: Some officers at this incident are firefighters. That conclusion is forced. The officers who are BA operators sit inside the firefighter circle. You do not get "all officers are firefighters" (the other officers may sit outside BA operators). You do not get "all firefighters are officers."

Worked could-be-true. Same premises. "Every firefighter at this incident is an officer" could be true in a tiny picture where the firefighter circle is exhausted by officer-BA people, and it could be false in a picture with a firefighter who is neither an officer nor named in the premises. Could-be-true is not a pass. If the stem asked what must follow, that conclusion is too strong.

Worked cannot-be-true. Same premises. "No officer at this incident is a firefighter" directly fights the overlap you already proved. Discard it.

Do not reverse universals

Illicit conversion is the most expensive habit on these items. All A are B does not mean all B are A. All pumpers are appliances. That puts every pumper inside the appliance circle. Aerials, tankers, and other appliances can still sit in the appliance circle outside the pumper circle. From "this vehicle is a pumper" you may conclude it is an appliance. From "this vehicle is an appliance" you may not conclude it is a pumper.

The same trap in salvage language: all salvage work is damage-control work. That does not make all damage-control work salvage. Overhaul, pumping out, and making-up can be damage-control without being salvage. Do not reverse the subset.

All A are B plus all B are C does chain: all A are C. All salvage covers are tarpaulins; all tarpaulins are waterproof sheets; therefore all salvage covers are waterproof sheets. That is a valid Barbara chain, not a reversal. The arrows still point the same way. Reversal would be concluding that all waterproof sheets are salvage covers.

No A are B is symmetric in a way all is not: if no defensive crews are interior, no interior crews are defensive. You may flip a genuine no. You may not flip an all.

Two 'some' statements do not chain

Some hydrants on this street are underground. Some water fittings on this street are hydrants. Those two overlaps need not be the same hydrants. The underground hydrants might be one subset. The hydrants that are water fittings in the second sentence might be a different subset (for example, pillar hydrants already above ground). You cannot conclude that some water fittings are underground. You also cannot conclude the opposite. The chained "some" is a could at best, and it is not a must.

Contrast that with a mixed chain that does work: All hydrants are water fittings. Some hydrants are underground. Therefore some water fittings are underground. The "all" forces every hydrant — including the underground ones — into the water-fitting circle.

Euler overlap you can hold in your head

Think of three labelled circles for the BA-operator example: BA operators sit entirely inside firefighters. Officers overlap BA operators in at least one person. That overlap person is an officer and a firefighter. The diagram block below is that picture, not a claim about QFD rank policy.

Valid versus invalid at a glance

Use the table as a drill sheet. The fireground nouns are replaceable; the quantifier pattern is not.

A head-only checklist

Run these steps when a stem dumps three sentences on you at once:

1. Mark each premise as all, some, or none. Do not upgrade some to all.
2. Draw two circles mentally for the first premise (subset, overlap, or disjoint).
3. Place the third group from the second premise. Ask whether it must sit inside, may sit inside, or must not sit inside.
4. Test the conclusion against a second legal picture. If you can redraw without breaking premises and the conclusion dies, it is not must-be-true.
5. Reject reversals of all. Allow the flip only for a genuine no.
6. Reject some-plus-some chains unless an all ties the same individuals together.
7. Ignore extra fireground facts (what a QFR officer "really" is, what salvage "usually" includes) unless a premise states them.
8. If the picture will not settle, skip and return if the Pearson interface still allows review.

A Gold Coast apartment fire can supply the nouns without supplying extra premises. "All BA operators on the landing are firefighters" is a subset. "Some officers on the landing are BA operators" is an overlap. "Some hydrants in the street are underground" is an overlap that does not, by itself, place every water fitting underground. Keep the incident as flavour. Keep the circles as logic.

Do not spend the last seconds inventing a published cut score. QFD has not released item counts or a percentage pass mark for Core Abilities. The pack says it is not expected that every question is answered correctly. A clean Euler picture on a must-be-true item is worth more than a guess dressed up as station experience.