Question: Using the Boolean algebra, if the following Boolean expression is minimized, then the result will be,\n\nAB + ABC + AB(D+E)\n\na) AB\nb) ABCD\nc) A\nd) ABC
1. **State the problem:**\nMinimize the Boolean expression $$AB + ABC + AB(D+E)$$ using Boolean algebra rules.\n\n2. **Recall important Boolean algebra rules:**\n- Idempotent Law: $$X + X = X$$\n- Absorption Law: $$X + XY = X$$\n- Distributive Law: $$X(Y + Z) = XY + XZ$$\n- Identity Law: $$X1 = X$$\n\n3. **Start simplifying the expression:**\n$$AB + ABC + AB(D+E)$$\n\n4. Notice that $$ABC$$ is a term with $$AB$$ and $$C$$, and $$AB$$ is a simpler term. Using the absorption law: $$AB + ABC = AB$$ because $$AB$$ absorbs $$ABC$$.\n\n5. Now the expression becomes:\n$$AB + AB(D+E)$$\n\n6. Factor $$AB$$ out:\n$$AB(1 + D + E)$$\n\n7. Using the identity law, $$1 + D + E = 1$$ because anything OR 1 is 1.\n\n8. So the expression simplifies to:\n$$AB \times 1 = AB$$\n\n9. **Final minimized expression:** $$AB$$\n\n**Answer:** a) AB