State and justify the validity of following inference rules

(i) Chain rule

(ii) Simplification

In the context of Artificial Intelligence (AI) and Knowledge Management (KM), inference rules are logical principles used to derive new facts or knowledge from existing information. These rules form the basis for reasoning in expert systems, decision support systems, and other AI-driven applications, as they help in automating the decision-making and problem-solving processes. The two rules in question, Chain Rule and Simplification, play essential roles in knowledge processing.

(i) Chain Rule

The Chain Rule is a fundamental rule of inference in logic and is used extensively in AI and KM systems, particularly in reasoning and rule-based systems. The Chain Rule operates on a sequence of logical implications and states that if we know that "P implies Q" (P → Q) and "Q implies R" (Q → R), we can infer ____ ________ ____ ______ ______.
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