Question

Find the duality of Boolean function 1.x+y’z+0

Answer 1

Answer:

Original expression: x+y'z+0

Dual of expression: x.y'+z.1

Explanation:

Principle of Duality states that starting from any boolean relation another boolean relation can be derived by

1) Changing each AND(.) to OR(+) and each OR(+) to AND(.).

2) Changing each 1 to 0 and 0 to 1.

Complement remaining the same.

The new expression derived by carrying out the above steps is called the Dual of the given boolean relation.

Process:

Following the principle of duality, each (+) is changed to (.) and each (.) is changed to (+).

Then 0 is changed to 1 while the complement (') remains the same.

Therefore, dual of the boolean relation x+y'z+0 is found out to be x.y'+z.1.

Also, if we further evaluate the above dual:

x.y'+z.1 = xy'+z (Properties of 1, p.1 = p)