Prove NOR is Complete: Logic Problem Solved

Thread starter zetafunction
Start date May 14, 2009
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Logic

In summary, 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. Proving NOR complete is important because it demonstrates the power and versatility of this single logical operator and helps to simplify logical systems. Other complete sets of logical operators include NAND, NOR, and a combination of NAND and NOR, but NOR is often considered the simplest complete set as it only requires one operator.

May 14, 2009

zetafunction

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

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May 14, 2009

Moo Of Doom

See if you can figure out NOT in terms of NOR (this is not too hard), then use DeMorgan's laws to figure out how to write AND and OR using NOT and NOR.

What is NOR?

NOR is a logical operator that produces a true output only if both inputs are false.

What does it mean for NOR to be complete?

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.

How can you prove that NOR is complete?

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.

Why is proving NOR complete important?

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.

Are there other complete sets of logical operators besides NOR?

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.