This problem is solved by linking the two statements to form a logical chain of events.

1. Premise 1: "Rakesh will go to the concert if his dog barks three times."
   This can be simplified to: IF the dog barks three times, THEN Rakesh will go.
2. Premise 2: "Rajesh will not go to the concert if Rakesh goes."
   This can be simplified to: IF Rakesh goes, THEN Rajesh will NOT go.
3. The Logical Chain: Combining these creates a direct sequence:
   (Dog Barks → Rakesh Goes → Rajesh Does NOT Go)
4. Valid Conclusion: By following the chain from the beginning to the end, we can make a new, true statement: IF the dog barks three times, THEN Rajesh will not go to the concert.

Evaluating the Options

• A, B, and D: These options represent logical fallacies (such as the inverse or the converse) and are not guaranteed to be true based on the given information. For example, we don't know what happens if the dog *doesn't* bark.
• C. "If Rakesh's dog barks three times, then Rajesh will not go to the concert."
  This statement perfectly matches the valid conclusion derived from our logical chain. This must be true.

Final Answer: The correct option is C because it is the only valid deduction that can be made by combining the two premises.