Which of the following Boolean algebra rule is correct?
Which of the following Boolean algebra rule is correct?
Answer: C. A + A’B = A+B — Option A (A⋅A′=1): Incorrect This violates the Complementarity Law. A variable AND its complement always equals 0 (e.g., 1⋅0=0). Correct rule: A⋅A′=0. Option…
- A.
A.A’=1
- B.
A + AB = A+B
- C.
A + A’B = A+B
- D.
A(A+B) =B
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Correct answer: C
Option A (A⋅A′=1): Incorrect
This violates the Complementarity Law.
A variable AND its complement always equals 0 (e.g., 1⋅0=0).
Correct rule: A⋅A′=0.
Option B (A+AB=A+B): Incorrect
This is an incorrect application of the Absorption Law.
We can factor out A from the expression: A(1+B).
Since (1+B)=1, the expression simplifies to A⋅1=A.
Correct rule: A+AB=A.
Option C (A+A′B=A+B): Correct
This is a standard simplification often derived using the Distributive Law.
You can expand the expression as: (A+A′)⋅(A+B).
Since (A+A′)=1, it simplifies to 1⋅(A+B), which equals A+B.
Option D (A(A+B)=B): Incorrect
This is another form of the Absorption Law.
Distributing A gives: A⋅A+A⋅B→A+AB.
Factoring A again gives A(1+B), which simplifies to A.
Correct rule: A(A+B)=A.