Consider the following statements regarding Boolean Logic:1.The Boolean identity A + A'B simplifies to A using absorption law principles.2.De Morgan’s theorem states (A + B)' = A'B' which is fundamental in logic transformation.3.Expression A + AB simplifies to A reducing redundant logic terms.Which of the above statements is/are correct?

Correct Answer: B - 2 and 3 only

Quick Concept Explanation

Boolean algebra uses exact identities for logic simplification. De Morgan transforms complemented sums/products, while absorption removes redundant terms; care is needed because A+A'B simplifies to A+B, not A. Key relation: (A+B)'=A'B'; A+AB=A; A+A'B=A+B.

Exam focus: Test a doubtful identity with a two-row truth assignment. Common trap: Absorption identities with a complemented term are easy to misremember.

Statement-wise Verification

• Statement 1 - Incorrect.
  The Boolean identity A + A'B simplifies to A using absorption law principles.
  A + A'B simplifies to A+B, not A
• Statement 2 - Correct.
  De Morgan’s theorem states (A + B)' = A'B' which is fundamental in logic transformation.
  De Morgan transforms complemented sums/products
• Statement 3 - Correct.
  Expression A + AB simplifies to A reducing redundant logic terms.
  Absorption removes redundant terms; care is needed because A+A'B simplifies to A+B, not A.

Core Concept

Boolean algebra uses exact identities for logic simplification. NAND and NOR are universal gates. AND is commutative and associative, and XOR is also associative. De Morgan transforms complemented sums/products, while absorption removes redundant terms; care is needed because A+A'B simplifies to A+B, not A.

Formula / Key Relationship

(A+B)'=A'B'; A+AB=A; A+A'B=A+B.

Why the Other Options Are Wrong

Option A is incorrect because it includes incorrect statement(s) 1 and omits correct statement(s) 3. Option C is incorrect because it includes incorrect statement(s) 1 and omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 1.

Exam Shortcut / Approach

Test a doubtful identity with a two-row truth assignment.

Common Mistake

Absorption identities with a complemented term are easy to misremember.

Quick Revision

De Morgan and Absorption Laws is linked with Simplification Laws, Boolean Algebra and Digital Electronics. Test a doubtful identity with a two-row truth assignment.