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how could i express using only the operator NOR (in logic) the rest of operation NOT(x) AND(x,y) OR(x,y) that is how i could prove that the Logic operator NOR is functionally complete
NOR is a logical operator that produces a true output only if both inputs are false.
In logic, a complete set of operators is one that can express all possible logical operations. This means that any logical statement or problem can be solved using only the NOR operator.
One way to prove that NOR is complete is by showing that it can be used to construct all other logical operators, such as AND, OR, and NOT. This is known as functional completeness.
Proving NOR complete is important because it demonstrates the power and versatility of this single logical operator. It also helps to simplify logical systems by reducing the number of operators needed.
Yes, there are other complete sets of logical operators, such as NAND, NOR, and a combination of NAND and NOR. However, NOR is often considered the simplest complete set as it only requires one operator.