The meaning of multi-class classification rules The meaning of multi-class classification rules

Example: I have two classification rules (Refund is a predictor and Cheat is a binary response):
(Refund, No) → (Cheat, No) Support = 0.4, Confidence = 0.57
(Refund, No) → (Cheat, Yes) Support = 0.3, Confidence = 0.43


=> multi-class classification rules:

(Refund, No) → (Cheat, No) v (Cheat, Yes)


When predicted classification for test data, (Cheat, No) will be selected priority so why we need to have (Cheat, Yes) in multi-class classification rules here?
(Cheat, No) will be selected (cheat will be classified as No) for the rule (Refund, No). 


In a binary response variable like cheat, all the information can be inferred from just the first rule: 

(Refund, No) → (Cheat, No) Support = 0.4, Confidence = 0.57 


The other rule is redundant. 

However, in the case of a multi-class response variable, we would like to have all the rules written out so we exactly know the likelihood of the rule implying each of the different classes in the response variable. To keep things consistent, this is also done for the case when the response variable is binary.