Conditional Reasoning II: "Unless," "Only If," Quantifiers & Chains
Recap: Extending Conditional Logic
Day 4 covered the basic sufficient/necessary mechanics. Today extends that into the forms that trip people up most in practice: "unless," quantified statements ("most," "some," "all"), and chains of multiple conditionals linked together.
CS Bridge
A unless B translates to ¬B → A (equivalently ¬A → B) — treat "unless" as "if not." Quantifiers map to ∀ and ∃: "all" and "every" are ∀ (and support conditional chaining), "some" is ∃ and means "at least one," "most" means "more than half" and, critically, gives you no valid inference when chained with another "most" claim (two overlapping majorities aren't guaranteed to overlap with each other). De Morgan's law shows up directly in "not both" (¬(A ∧ B) ≡ ¬A ∨ ¬B) and "neither...nor" (¬A ∧ ¬B).
1. "Unless," "Without," and "Until"
All three work the same way: whatever follows "unless" is the necessary condition for avoiding the negation of the rest of the sentence. "You can't graduate unless you pass the exam" → ¬Pass → ¬Graduate (equivalently, Graduate → Pass).
2. "No A Are B"
Translates to a conditional in both directions: A → ¬B and B → ¬A. These are contrapositives of each other, so you really only need one form.
3. "Some" and "Most"
"Some" means "at least one" — it does not preclude "all." "Most" means "more than half." Critically: "most" + "most" yields no guaranteed overlap (two different majorities of the same group could theoretically not share a single member if the group is large enough... actually in a finite group two majorities must overlap, but the test typically uses this to signal weak inference strength rather than zero inference — treat "most + most" claims as needing careful checking, not automatic combination). "All" + "most" does combine validly: if all A are B, and most C are A, then most C are B.
4. Valid Quantifier Combinations
The safe, always-valid chain is through universal ("all") statements: if All A → B and All B → C, then All A → C. The moment "most" or "some" enters a chain, check very carefully whether the combination is actually forced or just plausible-sounding.
5. Chaining Conditionals
When conditionals share a middle term, you can chain them like transitive relations: A → B and B → C gives A → C. This is how Sufficient Assumption and Must Be True questions often require you to link three or four conditionals to reach the answer.
6. Traps
The recurring trap here is treating "most" like "all" when chaining, and mistranslating "unless" in the wrong direction. Both produce a confidently wrong diagram that then produces a confidently wrong answer.
Practice items on this page are curriculum-authored in LSAT style; they are not official LSAC questions. Real drilling happens on LawHub — see the assignment below.
Original Practice Items
Q1. Translate: "The project cannot succeed unless the budget is approved by March."
Q2. Given "All certified auditors have passed the ethics exam" and "Most staff accountants are certified auditors," what follows?
Official Drill Assignment
LawHub free conditional-reasoning practice set (Official LSAT Prep lessons).
Peek into Tomorrow
Causal reasoning: a completely different kind of logic from conditionals — about explanations, not guarantees — and just as heavily tested across Flaw, Strengthen, Weaken, and Resolve-the-Paradox questions.