Any set of boolean operators that is sufficient to represent
2013
Any set of boolean operators that is sufficient to represent all boolean expressions is said to be complete. Which of the following is not complete? ISRO 2013
- A.
{NOT, OR}
- B.
{NOR}
- C.
{AND, OR}
- D.
{AND, NOT}
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Correct answer: C
A set of boolean operators is functionally complete if it can express all possible boolean functions. Universal gates like NAND and NOR are individually complete. Sets containing NOT along with AND or OR (e.g., {NOT, AND}) are also complete. However, the set {AND, OR} is not complete because it cannot generate the NOT operation. Without negation, one cannot express all truth tables (e.g., logical inversion). Thus, {AND, OR} is the incomplete set.