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CBSE Class 11 Computer Science Question 4 of 68

Data Representation and Boolean Logic — Question 4

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Question 4

Assertion (A): If A+B=1 then its dual will be A.B=0.

Reasoning (R): In dual, 1 changes to 0 and 0 changes to 1. Similarly, (+) changes to (.) and (.) to (+).

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Answer

Both A and R are true and R is the correct explanation of A.

Explanation
The dual of the Boolean expression A+B=1 is A⋅B=0. This is derived by applying the duality principle, which states that the dual of any boolean expression is obtained by interchanging the operations (+) and (.), and swapping the constants 1 and 0.