De Morgan's theorem provides relationships to simplify logic expressions. Which transformation is correct?

• A. ~(A · B) = ~A · ~B
• B. ~(A + B) = ~A + ~B
• C. ~(A · B) = ~A + ~B
• D. ~(A · B) = A · B

Answer: (C)

De Morgan's theorem states that negating a conjunction turns it into the disjunction of the negations. In other words, NOT(A AND B) is equal to (NOT A) OR (NOT B).

This transformation is the correct one because it preserves truth: if both A and B are true, the left side is false, and the right side is also false since both NOT A and NOT B are false; if either A or B is false, the left side becomes true, and at least one of NOT A or NOT B is true, making the right side true. This alignment holds for all combinations of A and B.

The other forms fail because they either keep the negation in the wrong place or apply the logical operators incorrectly. For example, NOT(A AND B) ≠ NOT A AND NOT B, and NOT(A OR B) ≠ NOT A OR NOT B (the latter would instead be NOT A AND NOT B). Also, ignoring the negation altogether would be incorrect.