Question

Find the dual of the Boolean function, f=A(B'C'+BC).​

Answer 1

Answer:

Dual of given boolean function will be,

$\sf{f^d = A + (B'+C') \;.\; (B + C)}$

Explanation:

Given Boolean expression is:

$\sf{f = A ( B' C' + B\;C)}$

We need to find its dual.

So,

The dual of a boolean expression or function can be derived by:

• Changing each OR sign (+) to AND sign (.)

• Changing each AND sign (.) to OR sign (+)

• Replacing each 0 by 1 and each 1 by 0

The dual of a function f is denoted by $\sf{f^d}$.

Therefore, following the given postulates of Principle of duality

Dual of boolean function f will be,

$\boxed{\sf{ f^d = A + (B' + C') \;.\; (B + C)}}$

the Principle of duality also states that

For two equal boolean functions f and g (f = g), the duals of functions f and g will also be equal $\sf{(f^d = g^d).}$