Discussion
Which Boolean identity is known as the idempotent law?
Answer: C
Correct answer: \( A + A = A \)
The idempotent law states that combining a variable with itself changes nothing: \[ A + A = A, \qquad A \cdot A = A. \] This is one of the clearest departures from ordinary arithmetic, where \( A + A = 2A \) and \( A \cdot A = A^{2} \). In a two-valued algebra there is no 2 and no square, so the operation simply returns the value unchanged. The other options are the remaining basic identities, each with its own name. \( A + \bar{A} = 1 \) is the complement law, with dual \( A \cdot \bar{A} = 0 \). \( A + 0 = A \) is the identity law, with dual \( A \cdot 1 = A \). And \( A + 1 = 1 \) is the null or annulment law, with dual \( A \cdot 0 = 0 \). Each pair is a dual of the other, obtained by exchanging AND with OR and 0 with 1 - a symmetry that runs through the whole of Boolean algebra and halves the amount to be memorised.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development