Question

Which of the following is NOT true about self-dual function? 
1. The function must be a neutral function.
2. The function must be equal to its dual
3. The function must not contain any mutually exclusive terms
4. The function must contain ‘n’ mutually exclusive terms

Answer 1

Correct Answer - Option 4 : The function must contain ‘n’ mutually exclusive terms

Self-dual function:

A function is said to be Self-dual if and only if its dual is equivalent to the given function, i.e.,

if a given function is f(A, B, C) = (AB + BC + CA) then its dual is, fd(A, B, C) = (A + B).(B + C).(C + A) (f_d = dual of the given function).

In a dual function, AND operator of a given function is changed to OR operator and vice-versa.

A constant 1 (or true) of a given function is changed to a constant 0 (or false) and vice-versa.

The necessary and sufficient conditions for any function to be a self-dual function are as follows:

1) The function must be a Neutral Function.

2) The function must not contain any mutually exclusive terms.

Hence the option (4) is correct

Neutral function:

Neutral function in which a number of minterms are equal to the number of max terms.

The number of neutral function possible are:  \(^{2^n}C_{2^{n-1}}\)

• For n variables, the total number of terms possible = number of combinations of n variables = 2n
• Since a maximum number of terms possible = 2n, so we choose half of the terms i.e 2n / 2 = 2n-1
• Thus, a number of neutral functions possible with n Boolean variables = C ( 2n, 2n-1 )
• The function does not contain two mutually exclusive terms.

 

Mutually exclusive terms:

A term obtained by complementing each variable of a function (f) is called its mutually exclusive term.

For example, (AB'C) → (A'BC')

A'BC' is a mutually exclusive term of AB'C.