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, $f^{d}(a, b, c) = (a + b).(b + c).(c + a)\;(f^{d} = $ dual of the given function$) = (ab + bc + ca),$ it is equivalent to the given function. So the function is self dual.
$\textbf{Dual function:}$ If the binary operators and the identity elements are interchanged, it is called the duality principle. We simply interchange OR and AND operators and replace $1’s$ by $0’s$ and $0’s$ by $1’s.$
$\textbf{(or)}$
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.
A Switching function or Boolean function is said to be Self dual if :
- The given function is neutral i.e., (number of min terms is equal to the number of max terms).
- The function does not contain two mutually exclusive terms.
$\textbf{Note:}$ Mutually exclusive term of $abc$ is $(\overline{a}\;\overline{b}\;\overline{c})$ i.e, compliment of $abc.$ So, two mutually exclusive terms are compliment of each other.
To generalize it we can say that in an $'n'$ variable function there should not be a pair whose sum is $= 2^{n-1}.$
So, the correct answer is $A;D.$
Reference:http://web.ee.nchu.edu.tw/~cpfan/FY92b-digital/Chapter2.pdf
