IGDTUW 2026 — Computer PYQ

The correct option is (a) Identity Law.

Detailed Solution

In Boolean algebra, laws are used to simplify complex logical expressions. The given equation is a fundamental identity property.

• Identity Law: This law states that ANDing any variable with '$1$' or ORing any variable with '$0$' returns the original variable itself. The value of the expression is completely dependent on the identity of the variable $A$.

  $$A\cdot 1=A$$

  $$A+0=A$$

Verification by Truth Table:

If we test the values of the variable $A$:

• If $A=0$, then $0\cdot 1=0$ (which equals $A$).

• If $A=1$, then $1\cdot 1=1$ (which equals $A$).

  In both cases, the output is identically equal to $A$.

Explanation of Other Options

• Idempotent Law: States that combining a variable with itself using AND or OR operations results in the original variable.

  $$A\cdot A=A$$

  $$A+A=A$$

• Complement Law: States that a variable combined with its inverse results in either '$1$' (for OR) or '$0$' (for AND).

  $$A+\bar{A}=1$$

  $$A\cdot \bar{A}=0$$

• Absorption Law: Involves absorbing a redundant variable into a simpler expression.

  $$A+(A\cdot B)=A$$

  $$A\cdot (A+B)=A$$