The following shorthand is
used in Lesson Sets:

K:3 : Shorthand for K appears third. This is most often used in sequences, but variations appear in "Grouping" and "Assignment" games as well. For example, “R:tu” might be used to indicate that the variable R is assigned to Tuesday. 

~P : Shorthand for “Not ‘P’”. Negation is one of the most important and widely used notations in formal logic, so you should become familiar with it. If you see "~P", it means there is no P. If you see “~M:7”, it means M is not
positioned 7th. 

P → Q :  This means if you have P, you must also have Q. This relationship is called a conditional relationship (as in, “if you have condition P, then you must also have condition Q”) or a causal relationship (as in “P causes Q”). Make sure you understand that this does not mean “Q means you must haveP”. (That relationship would be written Q → P.) You will often use the conditional arrow in conjunction with the negation symbol. For instance, the relationship “if on Wednesday you have X, then on Tuesday you cannot have Y” could be translated as “Wed: X → ~(Tue:Y)” or “Wed: X → Tue: ~Y”.  

P ↔ Q : This shorthand represents the “biconditional” relationship. The biconditional relationship is expressed by an “if and only if” statement. For example: “P is present if, and only if, Q is also present”. The double arrow means that the existence of one element in the biconditional relationship always implies the existence of the second element. 

[A, B] :   Shorthand for the Rule “A is positioned directly before B”. The comma indicates that the order is fixed (A appears before B). 

[A / B] :   Shorthand for the Rule “A is positioned next to B”. The slash notation is used because no order is given. You could have [A, B], or you could have [B, A]. 

A...B :   Shorthand for the Rule “A occurs sometime before B”. Note that the number of characters between A and B is unspecified. All this notation says is that “A” comes before “B”. 

[A,__,B] :   Shorthand for the Rule “A is positioned exactly one space
before B”. 

A...B/C :   Shorthand for the Rule “A is positioned before B and C”. The order of B and C is not stated, so they are separated with a slash. An alternative shorthand method is to break it into two Rules: A...B and A...C. However, this will make your shorthand more confusing and cluttered, and is therefore not recommended.  

A...[B, C] :   Shorthand for the Rule “A is positioned before B, which is placed directly before C”. This notation is most often used when combining Rules, but sometimes results from a single Rule. 

[A/B, __, B/A] :   Shorthand for the Rule “There is exactly one package between A and B, whether or not A is delivered before B”. An alternative shorthand method is write out both possibilities: [A, __, B] or [B, __, A]. You will also see variations of this shorthand that include more space in between the characters. For example, the Rule “there are exactly two students between Becky and Chris” would be translated into shorthand as
[B/C, __, __, C/B]. 

A/ :   This indicates a possible position for a variable. For example, if you know that “Z” must be placed in slot 3 or 7, you can place a Z/ underneath the third and seventh slots of your model.  

Not Consec :  This means that characters do not appear consecutively. For instance, a Rule might state "no boys in the group can appear consecutively".  

Each x1+ :  This shorthand denotes the requirements for the number of times that each character must appear. In this case (“Each x1+”), each character must appear at least once. Variations on this notation include Each x2 Max, Each x2, x3 Max.