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Course: LSAT > Unit 1
Lesson 3: Analytical Reasoning – Articles- Getting started with Analytical Reasoning
- How to approach ordering setups
- How to approach grouping setups
- How to approach mixed setups
- Given info: basic orientation | Quick guide
- Given info: could be true/false | Quick guide
- Given info: must/cannot be true/false | Quick guide
- New info: could be true/false | Quick guide
- New info: must/cannot be true/false | Quick guide
- Equivalent rule, min-max and completely determines | Quick guide
- Equivalent rule | Learn more
- Study plan for analytical reasoning | Getting more than 10 right
- How to use multiple scenarios in analytical reasoning setups
- Deductions in analytical reasoning | Introduction
- Deductions in analytical reasoning | Practice
- Diagram notation conventions for analytical reasoning setups
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Diagram notation conventions for analytical reasoning setups
Google ClassroomDiagram 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.
A is before/above, but not necessarily immediately before/above, B.
A is immediately before/above B.
A and B are a pair (next to each other), but we don’t know in what order.
A is earlier than B, with at least one element between them.
A is earlier than B, with exactly one element between them.
A is sometime earlier than B, and A is also sometime earlier than C.
A can never be immediately before B.
A and B can never be next to each other, regardless of the order.
The same elements can never be consecutive.
There are least two spots, up to a maximum of four spots.
Placement, or assignment notations
A can never be in spot 1.
Either A or B must be in spot 1.
A must be in either spot 1 or 4.
A must be in either spot 3 or 4.
A and B are somewhere in spots 2, 3, and 4, but we don’t know which ones, and we don’t know in what order.
A and B are a pair, and they are either in spots 2 and 3, or in spots 3 and 4, respectively.
A is sometime before B, though not necessarily immediately before B, and that relationship takes place somewhere between spots 2 and 4 inclusively.
We’ve tested out A in 3 and B in 4, but it breaks one of the other rules.
The same element must go into spots 1 and 4.
The elements in spots 1 and 4 must be different from each other.
Grouping notations
For more on grouping setups specifically, you can consult the article How to approach grouping setups.
The elements will be grouped into categories X, Y, and Z, and we know that each category will have at least one element.
The elements will be grouped into categories X, Y, and Z, and we know that each category will have at least one element, but that category X has only one element.
A can never be assigned to group X.
Neither A nor B can be in group X, but they also can’t be a pair—in other words, one of A and B is in group Y, and the other of A and B is in group Z.
A and B are a pair—in other words, they’re both in the same category/group.
A and B cannot be a pair—in other words, they can’t be in the same category.
If A is in group X, then B must be in group Z.
There are fewer elements in group X than there are in group Z.
There are fewer of element A present than there are of element B, but there's at least one of each type of element.
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.
Conditional rules about groups
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.
Conditional rules about placement
- 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.
Conditional rules about quantity
- 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?(3 votes)
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."(3 votes)
Under "Conditional rules with AND/OR," it says "We can infer that AB will never be a pair, and AC will never be a pair." But couldn't they technically be a pair if they were both not in the selected category (not A & not B or not A & not C)?(2 votes)- I agree with you.
o If Art is selected, then neither Biology nor Chemistry can be selected.
o If Art is selected, then Biology cannot be selected and Chemistry cannot be selected.
o We can infer that Art and Biology will never be a pair, OR Art and Chemistry will never be a pair.
If Biology is selected, then Art is definitely not selected. However, chemistry doesn't conflict with any rules. Chemistry could be selected or not be selected. If B => -A, then we cannot deduct anything about C. Assume there are only two categories, C could be in the same category as B, or C could be in the same category as A. C cannot be decided to be or not to be with A.
The same applies if C => -A, then B cannot be decided to be or not to be with A.(1 vote)
- When you have a rule that is a is before b, it can be written like a...b. How many options can be between them? If you worked out a problem and you put a and b next to each other, is that breaking a rule? Would that make them a pair? Thanks! :D(1 vote)