Understanding Action and Reaction
The statement "Action and reaction are equal and opposite but even then they do not cancel each other" reflects an important principle in Newton's Third Law of Motion. Let's explore this concept in detail.

Newton's Third Law of Motion
- This law states that for every action, there is an equal and opposite reaction. This means that when one body exerts a force on another, the second body exerts a force of equal magnitude but in the opposite direction on the first body.

Why They Don’t Cancel Each Other
- **Different Objects**: The forces act on different objects. For example, when you push against a wall (action), the wall pushes back with the same force (reaction). Both forces do not act on the same body, hence they do not cancel each other out.
- **Net Force**: The cancellation of forces is only possible when they act on the same object. In the case of action and reaction forces, since they are always acting on different objects, they contribute to the motion of those respective objects.

Examples in Everyday Life
- **Walking**: When you walk, your foot pushes backward against the ground (action), and the ground pushes your foot forward (reaction). These forces enable your movement but do not cancel out because they act on different entities.
- **Rocket Propulsion**: A rocket expels gas downward (action), and the gas pushes the rocket upward (reaction). Again, the forces do not cancel because they are acting on different systems.

Conclusion
- Therefore, the statement is true. Action and reaction forces are equal and opposite; however, they do not cancel each other because they act on different objects. Understanding this principle is crucial in physics and helps explain various real-world phenomena.