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[Boolean Algebra]

Assertion (A): In Boolean Algebra, dual of the Boolean expression (A + B)’ . 1 is equal to 0.

Reason (R): In Boolean Algebra, the complement of an OR operation is equal to the AND operation of complement of the individual variables.

ID: #24955 Competency focused Practice Questions ISC Class XII Computer Science 4 views

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A Both A and R are true, and R is the correct explanation of A. ✔ ✖
B Both A and R are true, but R is not the correct explanation of A. ✔ ✖
C A is true, but R is false. ✔ ✖
D A is false, but R is true. ✔ ✖

Correct Answer: Option D

Explanation

[Boolean Algebra]

Assertion (A): In Boolean Algebra, dual of the Boolean expression (A + B)’ . 1 is equal to 0.

Reason (R): In Boolean Algebra, the complement of an OR operation is equal to the AND operation of complement of the individual variables.

(a) Both A and R are true, and R is the correct explanation of A.

(b) Both A and R are true, but R is not the correct explanation of A.

(d) A is false, but R is true.

Correct Answer: (d)

Step 1: Understanding the Assertion (A)

Dual of (A + B)’ . 1 is equal to 0

What is Dual in Boolean Algebra?

To find the dual:

Replace OR (+) with AND (.)
Replace AND (.) with OR (+)
Replace 1 with 0
Replace 0 with 1

Given Expression:

(A + B)’ . 1

Applying Dual Rules:

Original	Dual
+	.
.	+
1	0

Therefore:

Dual of (A + B)’ . 1 = (A . B)’ + 0

Since:

X + 0 = X

Final result becomes:

(A . B)’

It is NOT equal to 0.

Therefore:

Assertion (A) is FALSE

Step 2: Understanding the Reason (R)

Complement of OR operation equals AND operation of complements of individual variables.

This is known as De Morgan’s Theorem.

(A + B)’ = A’ . B’

This statement is absolutely correct.

Reason (R) is TRUE

Important Concept:

Law	Expression
De Morgan’s First Law	(A + B)’ = A’ . B’
De Morgan’s Second Law	(A . B)’ = A’ + B’

Final Conclusion:

Assertion (A) → False ❌
Reason (R) → True ✅

Correct Answer: (d)

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Q [Boolean Algebra] Assertion (A): In Boolean Algebra, dual of the Boolean expression (A + B)’ . 1 is equal to 0. Reason (R): In Boolean Algebra, the complement of an OR operation is equal to the AND operation of complement of the individual variables.