Conditional Logic Basics

Flashcards covering fundamental conditional reasoning concepts from the lecture.

Sufficient Condition

The “if” part of a conditional; a circumstance that, when present, guarantees the necessary condition; placed on the left side of the arrow (X → …).

Necessary Condition

The requirement that must be satisfied whenever the sufficient condition occurs; signaled by words like “only if,” “must,” or “requires,” and placed on the right side of the arrow (… → Y).

Conditional Statement

A logical rule expressed as “If X, then Y,” diagrammed X → Y, linking a sufficient condition to a necessary one.

Contrapositive

The logically equivalent form of a conditional obtained by flipping the terms, negating both, and swapping AND with OR (X → Y becomes ¬Y → ¬X).

AND/OR Flip Rule

When forming a contrapositive, every “and” becomes “or” and every “or” becomes “and.”

Biconditional

A two-way conditional triggered by phrases like “if and only if” or “just in case”; both X → Y and Y → X, diagrammed X ↔ Y.

“Only if”

Keyword that introduces a necessary condition; what follows must appear on the right side of the arrow.

“Unless / Without / Until / Except”

Negative-condition indicators translated using the “IF NOT” rule: e.g., “Unless A” becomes “If not A.”

Arrow Reversal Fallacy

The invalid mistake of reading a conditional backwards—treating the necessary condition as sufficient (Y → X from X → Y).

Illegal Negation

Fallaciously inferring that the absence of the sufficient condition guarantees the absence of the necessary condition (¬X → ¬Y).

Prerequisite

A requirement that must be in place before something else can occur; diagrammed Result → Prerequisite (e.g., Run → Learn to Walk).

Compound Statement Negation

Correctly negating A ∧ B as ¬A ∨ ¬B, and A ∨ B as ¬A ∧ ¬B; essential when making contrapositives.

Yale Admissions Example

“You can’t get into Yale without a great LSAT score” translates to Yale → Great LSAT, not the reverse.

Breath Strips Example

“Using breath strips instead of mints is the only way to be cool” translates to Cool → Use Breath Strips.

Practical Uses of Conditional Logic

Skills honed on LSAT conditional reasoning apply to legal arguments, contracts, and everyday decision-making.