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Boolean Algebra
f-alpha.net » Mathematics » Algebra » Boolean Algebra » Let's go... » Experiment 6 - Identity

Experiment 6 - The Identity (Neutral Element)

AND operation

The neutral element of the AND operation is 1...

$$A \wedge 1 = A$$

Logical diagram neutral element of an AND operation.

A logic circuit neutral element of an AND operation. (Enlarge)

OR operation

The neutral element of the OR operation is 0...

$$A \vee 0 = A$$

Logical diagram neutral element of an OR operation.

A logic circuit neutral element of an OR operation. (Enlarge)

Comparison Arithmetic - Boolean Algebra

Also the addition and multiplication have neutral elements...

$$x + 0 = x \quad\mbox{and}\quad x \times 1 = x $$

As already mentioned, the AND operation is similar to the multiplication and the OR operation is similar to the addition!

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