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# Diagram notation conventions for analytical reasoning setups

## Diagram notation conventions for Analytical Reasoning setups: a quick guide

This article provides an inventory of the notations you will see throughout the Analytical Reasoning setups here at Khan Academy’s Official LSAT Practice. We consider these notations to be one set of “best practices”. That said, there is no “right way” of notating setups and their rules, and you should feel free to develop a system that works for you.
Whichever notations you wind up using, we strongly recommend that you arrive at a set of conventions that you like, and then practice using them efficiently and consistently as you prepare to do your best on Test Day.

### Ordering notations

For the first two examples, we’ll show you the notation for a horizontal diagram on the left, and a vertical diagram on the right. For the remaining examples, we’ll show you how we’re notating the relationship in a horizontal ordering setup, and you can infer what the corresponding vertical-diagram notation would look like.
For more on ordering setups specifically, you can consult the article How to approach ordering setups.

### Grouping notations

For more on grouping setups specifically, you can consult the article How to approach grouping setups.

### Conditional notations

Note: the second notation in each rule is a logically equivalent version of the stated rule (also known as the
). For more on logically equivalent rules, you can consult the article Conditional reasoning and logical equivalence.

Examples:
• If A is selected, B is also selected.
• If A is in a category, B must also be in that category.
• A is in a category only if B is in that category.
• A cannot be selected unless B is also selected.
• B must be selected in order for A to be selected.

• If A is in spot 2, then B must be in spot 3.
• A can be in spot 2 only if B is in spot 3.
• A can’t be in spot 2 unless B is in spot 3.
• B must be in spot 3 in order for A to be in spot 2.

• If two A elements are present, then three B elements must also be present.
• The only way that two A elements can be selected is if three B elements are selected.
• Two A elements are present only if three B elements are present.
• Three B elements must be selected in order for two A elements to be selected.
• Two A elements cannot be present unless three B elements are present.

#### "If and only if"

• A is selected if and only if B is selected.

#### Conditional rules with AND/OR

• If A is selected, then B cannot be selected and C cannot be selected (or, if A is selected, then neither B nor C can be selected).
• In setups with categories, if A is part of a category, then neither B nor C can be part of that category.
• We can infer that AB will never be a pair, and AC will never be a pair.

#### Conditional rules with mixed notation

• If A is earlier than B, then C cannot be in spot 3.
• The logically equivalent rule is that if C is in spot 3, then either B is before A, or B and A are at the same time.

## Want to join the conversation?

• Are these the same notations they teach in law school?
• There appears to be a typo in the last note of the "If and only if" section, namely the "if [A]" in "in setups with categories, this notation means that if A is part of a category if and only if B is also part of that category."