Which of the following is the complement of the boolean function.…
2025
Which of the following is the complement of the boolean function.
A'B+CD'+A'B+CD'
- A.
A'B+CD'
- B.
(A'+B)(C+D')
- C.
(A+B')(C'+D)
- D.
A(C' + D)
Attempted by 298 students.
Show answer & explanation
Correct answer: C
Step 1: Simplify the expression
Notice the terms are repeated:
A′B+A′B=A′B
CD′+CD′=CD′
So,
F=A′B+CD′
Step 2: Take Complement
F′=(A′B+CD′)
Apply De-Morgan’s Law:
F′=(A′B)′⋅(CD′)′
Step 3: Complement each part
(A′B)′=A+B′
(CD′)′=C′+D
Step 4: Final Answer
F′=(A+B′)(C′+D)
Correct Complement
👉 (A + B')(C' + D)
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