NIMCET 2013 — Computer PYQ

We can use the properties of Boolean Algebra to simplify this expression:

1. Commutative Law: Rearrange the terms:

   $$x+\bar{x}+\bar{y}$$

2. Complement Law: Any variable ORed with its complement is always $1$:

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

3. Identity Law: Substitute $1$ back into the expression:

   $$1+\bar{y}$$

4. Annulment Law: Anything ORed with $1$ is always $1$:

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

Since the final result is a constant $1$ regardless of the values of $x$ or $y$, it is a tautology.