A Quick Guide to Conditional Logic — Khan Academy

Source: Khan Academy / LSAT prep series Raw file: raw/A quick guide to conditional logic (Khan Academy).md

Summary

A reference guide for translating 14 common prose phrasings into conditional logic diagrams. The core insight: the same logical structure (X → Y) hides behind many different surface phrasings in natural language. Accurate translation requires reading for logical meaning, not word-by-word parsing.

The 14 Translation Patterns

High-risk translations (most commonly mistranslated):

• "X if Y" → Y → X (not X → Y). The word "if" points to the sufficient condition, which is Y here.
• "Only X are Y" → Y → X. "Only" signals the necessary condition — only X can be Y means being Y requires being X.
• "X happens whenever Y" → Y → X. "Whenever" makes Y the trigger.
• "No X unless Y" → X → Y. "Unless Y" means "if not Y, then not X" — equivalently, X requires Y.

Key Takeaways from the Source

Trigger → Result: The left side of the arrow is the trigger (sufficient condition). If it's true, the right side is guaranteed 100% of the time. Timeline is irrelevant — only the direction of sufficiency matters.

Translate logical meaning, not words: "X if Y" does not map X on the left just because X appears first. Read what the sentence is claiming before assigning positions.

Contrapositives are always included: Every translation comes with its logically equivalent contrapositive. Knowing both is necessary for test reasoning because the trigger you're given is often the contrapositive trigger, not the original.

Concepts

• sufficient-and-necessary-conditions — every translation pattern in this guide is an instance of the sufficient/necessary distinction; the table expands the concept's signal-word section with 14 concrete prose forms