Let A'represent complement of A . Which of the following boolean expressions is/are true? (A) \( A+AB=A \) (B) \( (A+B) =A B \) (C) \( (A ) =A \) (D) \( (AB) =A +B \) Choose the correct answer from the options given below:

Check each identity: (A) \(A + AB = A(1 + B) = A\). True (absorption law). (B) \((A+B)' = A'B'\). True (De Morgan's law). (C) \((A')' = A\). True (involution). (D) \((AB)' = A' + B'\). True (De Morgan's law). All four are true. Answer: (C) (A), (B), (C) and (D)

Let A'represent complement of A . Which... - Solved

Question 27

Computer Awareness Binary Logics Hard

Let A'represent complement of A . Which of the following boolean expressions is/are true?

(A) \( \mathrm{A}+\mathrm{AB}=\mathrm{A} \)

(B) \( (\mathrm{A}+\mathrm{B})^{\prime}=\mathrm{A}^{\prime} \mathrm{B}^{\prime} \)

(D) \( (\mathrm{AB})^{\prime}=\mathrm{A}^{\prime}+\mathrm{B}^{\prime} \)

Choose the correct answer from the options given below:

(A) (A), (B) and (D) only

(B) (A) and (D) only

(C) (A), (B) , (C) and (D)

(D) (B) and (D) only.

✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Check each identity:

(A) \(A + AB = A(1 + B) = A\). True (absorption law).
(B) \((A+B)' = A'B'\). True (De Morgan's law).
(C) \((A')' = A\). True (involution).
(D) \((AB)' = A' + B'\). True (De Morgan's law).

All four are true.

Answer: (C) (A), (B), (C) and (D)

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Question 27

📘 Step-by-Step Solution & Detailed Explanation:

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