Conditional Diagramming Part III: “If But Only If” in LR Questions

The Two Rules

Whether the phrase uses the word “and” or the word “but,” the following two rules are expressed:

1. A will attend the party if B attends: B → A
2. A will attend the party only if B attends: A → B

These two rules can be concisely expressed together with a double arrow:

A ↔ B

The Contrapositives

As discussed in the PowerScore LSAT Logical Reasoning Bible, the contrapositives of the two statements above are as follows:

1. If A does not attend the party, B will not attend: NOT A → NOT B
2. If B does not attend the party, A will not attend: NOT B → NOT A

Again, the two contrapositives can be expressed more concisely with a double arrow:

NOT A ↔ NOT B

In the end, this rule tells us that either both A and B will be at the party, or neither one will be there.

P.S. If a future LSAT game happens to include the rule “C will attend if, yet only if, D attends,” don’t be thrown off! Recognize this as just another clever rephrasing of the very same rule.

More on Conditional Diagramming

• “Or” in the Sufficient Condition
• “And” in the Necessary Condition
• Working with “Only”
• Advantages of the Unless Equation