(A) : According to Newton's third law sum of action and reaction is not equal to zero
(r) : The forces action and reaction acts on different bodies

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
C. (A) is true but ( R) is false
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze the two statements given:

(A): According to Newton's third law, the sum of action and reaction is not equal to zero.
(r): The forces action and reaction act on different bodies.

### Step-by-step Solution:

1. **Understanding Newton's Third Law**:
Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one body exerts a force on a second body (action), the second body exerts a force of equal magnitude but opposite direction on the first body (reaction).

**Hint**: Recall the basic principle of action and reaction forces.

2. **Analyzing Statement (A)**:
The assertion states that the sum of action and reaction is not equal to zero. Since action and reaction forces act on different bodies, they do not cancel each other out. Therefore, while the magnitudes of the forces are equal, their vector sum is not zero because they act on different objects.

**Hint**: Think about how forces interact with different bodies and why they don't cancel out.

3. **Analyzing Statement (r)**:
The reason states that the forces of action and reaction act on different bodies. This is indeed true, as action and reaction forces are always exerted on different objects. Thus, they do not cancel each other out.

**Hint**: Consider the implications of forces acting on separate bodies.

4. **Conclusion**:
Both statements (A) and (r) are true. Furthermore, statement (r) correctly explains statement (A) because the reason given clarifies why the assertion is valid.

Therefore, the correct answer is: **Both A and R are true, and R is the correct explanation of A**.

### Final Answer:
Both A and R are true, and R is the correct explanation of A.