JAMIA 2024 — Computer PYQ

Mathematical Proof

To see how we get from the option to the reduced form, we use the following Boolean laws:

1. Distributive Expansion:

   $$(A+B)(A+C)=A\cdot A+AC+AB+BC$$

2. Idempotent Law ($A\cdot A=A$):

   $$A+AC+AB+BC$$

3. Absorption Law ($A+AB=A$ and $A+AC=A$):

   By factoring out $A$:

   $$A(1+C+B)+BC$$

   Since $(1+\text{anything})=1$:

   $$A(1)+BC$$

4. Final Reduced Form:

   $$A+BC$$