Conditional Rules in LSAT Logic Games: How to Read, Diagram, and Chain Them

A conditional rule is any rule that says 'if X, then Y' — or something logically equivalent to that. In LSAT Logic Games, these rules are everywhere. Grouping games use them to restrict membership. In/out games are almost entirely built from them. Even sequencing games often include one or two conditional placement rules.

The reason conditional rules are so central is that they create the most interesting deductions. A single conditional rule applied twice can fix four or five entities simultaneously. Students who can read and chain conditional rules quickly have a decisive advantage.

A conditional rule has two parts: a sufficient condition (the trigger) and a necessary condition (the result). If the sufficient condition is true, the necessary condition must also be true.

Standard form: 'If A is selected, then B is not selected.' Sufficient: A selected. Necessary: B not selected. Arrow: A → ¬B.

The sufficient condition does not have to come first in the sentence. 'B is not selected if A is selected' says the same thing. 'B is not selected whenever A is selected' says the same thing. 'A is selected only if B is not selected' also says the same thing. Always identify the trigger (the sufficient condition) and the result (the necessary condition), regardless of word order.

The contrapositive of A → B is ¬B → ¬A. Both are equally valid. Both are tested.

For every conditional rule you write down, immediately write the contrapositive on the next line. No exceptions. Skipping this step under time pressure causes one common, painful error: on a question that requires the contrapositive direction, you re-derive it from scratch and make an algebra mistake.

'If A is selected, B is not.' A → ¬B. Contrapositive: B → ¬A. Done. Two lines, ten seconds.

'If the red block is used, the blue block and the green block are both used.' R → B and R → G. Contrapositive: ¬B → ¬R; ¬G → ¬R. Write all four lines.

'If A, then B' → A → B. Standard form.

'A only if B' → A → B. The term after 'only if' is the necessary condition.

'Unless B, not A' → A → B (equivalent to: if not B, then not A, which contraposes to A → B).

'A and B are not both selected' → A → ¬B (and B → ¬A). Both contrapositives say the same thing because the rule is symmetric.

'A cannot be selected without B' → A → B.

'Whenever A is selected, C is also selected' → A → C.

The surface language varies, but the underlying structure is always: identify the trigger, identify the result, draw the arrow, write the contrapositive.

The most powerful Logic Games deduction is a conditional chain: if rule 1 says A → B and rule 2 says B → C, then A → B → C is a valid chain. Selecting A forces both B and C.

Chains work in both directions. The contrapositive chain of A → B → C is ¬C → ¬B → ¬A: excluding C forces B out and A out.

Look for shared middle terms when scanning the rules. If you see 'A → B' and 'B → C' and 'C → D,' the full chain is A → B → C → D. Selecting A triggers a cascade of four placements.

Also look for closure: a chain where the end point contradicts the starting point. If A → B → ¬A, then A can never be selected (selecting it produces a contradiction). This eliminates entire scenarios without any question-specific information.

Conditional rules in sequencing games usually govern placement rather than selection: 'If A is in slot 1, then B is in slot 3.' These translate the same way: A₁ → B₃. Contrapositive: ¬B₃ → ¬A₁.

A common sequencing variant: 'If A comes before B, then C comes after D.' This is a conditional about relative order. Diagram it as: A precedes B → C comes after D. Contrapositive: D comes before or equal to C → B comes before or equal to A (using the negation of 'C comes after D' and 'A comes before B').

Conditional ordering rules are harder to chain than placement rules, but the same logic applies. Look for rules that share an entity or a slot and see what combined constraint they create.

Several question types test conditional rules explicitly. 'Which of the following must be true?' often tests the contrapositive of a rule you may not have written down. 'Which of the following cannot be true?' tests whether a selection would trigger a contradictory chain. 'If A is selected, which of the following must also be true?' asks you to apply the chain starting from A.

All of these become easy if your conditional rules and their contrapositives are already recorded on your diagram. They become time-consuming if you are deriving them during the question.

Verbloom's logic games drills include targeted conditional-chain practice, where you are shown a rule set and asked to identify the valid inferences before any questions appear. This isolates the skill and builds it faster than solving full games alone. Try the free section at verbloom.dev.