"If and Only If" on the LSAT: Diagramming Biconditionals

"A if and only if B" combines two conditionals: "if A then B" and "if B then A." The arrow runs both directions. The condition is met exactly when both sides match — both present or both absent.

Contrast this with a plain "if," which runs one direction only. Treating a one-way rule as two-way is a classic LSAT trap, and "if and only if" is the rare phrase that genuinely licenses the two-way reading.

Write a double arrow: A <-> B. That captures both A then B and B then A. The contrapositive is also two-way: not-A <-> not-B.

Equivalent phrasings to watch for: "exactly when," "all and only," and "is both necessary and sufficient for." Each signals a biconditional.

"A bill becomes law if and only if the governor signs it." Diagram: Law <-> Signed. So signing guarantees it becomes law, and becoming law guarantees it was signed. No bill becomes law unsigned, and no signed bill fails to become law.

Verbloom's conditional engine treats biconditionals as a distinct symbol so you never accidentally collapse a two-way rule into one direction.