Boolean Advanced Quiz 5

1. What mathematical operation calculates the derivative-like evaluation of a function relative to a coordinate change: $f_{x_i} \oplus f_{\bar{x}_i}$?

2. What mathematical term describes a Boolean function that is strictly equivalent to its own truth-value dual?

3. Which theorem proves that any finite Boolean algebra must have a cardinality that is exactly a power of two?

4. In modern electronic design automation, what matrix type handles the row-by-column tracking of prime implicants against target minterms?

5. What operational name is given to the variable abstraction method defined by the expression $f(x=1) \cdot f(x=0)$?

6. What operational name is given to the variable abstraction method defined by the expression $f(x=1) \lor f(x=0)$?

7. Which mathematical property states that a Boolean algebra is structurally isomorphic to its completely inverted dual system?

8. In the structural analysis of circuits, what classification describes a prime implicant that can be dynamically excluded without changing functional coverage?

9. What is the total number of distinct n-ary Boolean operations that can theoretically exist for a system with exactly two independent variables?

10. Which relational operator orders a Boolean lattice, matching the physical containment properties found in a standard fields-of-sets system?