Match the Boolean-algebra laws to their relational forms: (A) Distributive law, (B) De Morgan’s law, (C) Idempotent law, (D) Involution law — with (1) x + x = x, (2) x(y + z) = xy + xz, (3) (x)̄̄ = x, (4) (x + y)̄ = x̄ ȳ.

Introduction:Boolean algebra laws provide the algebraic toolkit for simplifying logic expressions and designing digital circuits. This item tests recognition of four cornerstone identities and their canonical forms.

Given Data / Assumptions:

• A: Distributive law.
• B: De Morgan’s law.
• C: Idempotent law.
• D: Involution (double-complement) law.
• Relational forms: (1) x + x = x, (2) x(y + z) = xy + xz, (3) (x)̄̄ = x, (4) (x + y)̄ = x̄ ȳ.

Concept / Approach:

Each law has a standard, widely used expression. The distributive law expands products over sums. De Morgan’s laws transform complements of sums/products. Idempotence states redundancy of combining a variable with itself. Involution states that complementing twice restores the original variable.

Step-by-Step Solution:

Verification / Alternative check:

Truth tables or Venn diagrams confirm each identity; Karnaugh maps also illustrate idempotence and distributivity.

Why Other Options Are Wrong:

Any permutation that mismatches these canonical forms contradicts standard Boolean identities taught in digital logic.

Common Pitfalls:

Confusing De Morgan’s transformations or mixing the two De Morgan forms; forgetting that idempotence applies to both + and · operations.

Final Answer:

A-2, B-4, C-1, D-3