a$.$ If there are n binary inputs associated with a decision, how many rules will be generated in the full $($i$.$e$.,$ before compression$)$ decision table? $(5$ points$)$

b$.$ Suppose a decision table containing $16$ rules was compressed to a table with $8$ rules. These dash entries are such that every row of the table has exactly one dash entry $($i$.$e$.,$ there is no dominant input in the compressed table$).$ How many inputs $($or input rows$)$ are there in this problem? $(5$ points$)$

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c$.$ A full $($or uncompressed$)$ decision table generates the same table after compression. In other words, no compression is possible for this table. We are seeking to construct a decision tree that has the least expected cost. Is the following claim true or false? $(5$ points$)$

All decision trees generated for this problem will be optimal.