CUET PG 2024 — Computer PYQ

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Question

CUET PG 2024 — Computer PYQ

CUET PG | Computer | 2024

Let A' represent complement of A. Which of the following Boolean expression 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:

Choose the correct answer:

Explanation

Evaluation of Expressions

(A) $A + AB = A$

Yeh Absorption Law hai.

A + AB = A(1 + B)

Chunkee $1 + B = 1$ , isliye:

A(1) = A

\therefore \text{True}

(B) $(A + B)' = A'B'$

Yeh De Morgan's First Law hai. Iske anusar, kisi sum ka complement unke individual complements ke product ke barabar hota hai.

\therefore \text{True}

(C) $(A')' = A$

Yeh Double Negation (Involution) Law hai. Kisi variable ko do baar invert karne par wahi original variable milta hai.

\therefore \text{True}

(D) $(AB)' = A' + B'$

Yeh De Morgan's Second Law hai. Iske anusar, kisi product ka complement unke individual complements ke sum ke barabar hota hai.

\therefore \text{True}

Final Conclusion

Chunkee chaaro expressions (A, B, C, aur D) Boolean algebra ke sahi niyam (laws) hain:

\text{Correct Answer} = \text{(A), (B), (C), and (D) all are true.}