Question

Give the relationship that represents the dual of the Boolean Property A+1=1?
(Note: * = AND, + = OR, ‘= NOT)
(A) A*1=1
(B) A*0=0
(C) A+0=A
(D) A*A=A
(E) None of these

Answer 1

Hint: We start solving this question by first discussing the concept of Boolean expression and the dual of a Boolean expression. Then we find the dual of the given expression by changing ‘+’ to ‘*’ and ‘1’ to ‘0’. Then we substitute these new symbols in place of the old symbols in the given Boolean identity to find the dual of the given Boolean identity.

Complete step by step answer:
First, let us go through the concept of a Boolean expression.
A Boolean expression is a logical statement that is either TRUE or FALSE, that is it takes the values 1 or 0.
Now, let us go through the concept of dual of a Boolean expression.
The dual of a Boolean expression is the expression one obtains by interchanging addition and multiplication and interchanging 0’s and 1’s in the expression.
So, for any Boolean expression,
‘+’ in the expression is changed to ‘*’ and ‘*’ is changed to ‘+’.
‘0’ in the expression is changed to ‘1’ and ‘1’ is changed to ‘0’.
The Boolean identity we are given is A+1=1.
So, as we see the above expression has symbols ‘+’ and ‘1’.
As we need to find the dual of the given Boolean identity, ‘+’ in the expression should be changed to ‘*’ and ‘1’ should be changed to ‘1’.
So, by changing them we get, A*0=0.
So, the correct answer is “Option B”.

Note:
 The common mistake one makes in this question is one might only convert the given expression into its dual by changing ‘+’ in the expression to ‘*’ only and writing the dual as A*1=1 and marking the answer is Option A.