Let P (x) and Q(x) be two predicates and suppose D is the the domain of For the statement forms in each pair, determine whether they have the same truth value for every choice of p(x), Q(x) and D, or not. ∀x ∈ D, (P (x) ∧ Q(x)), and (∀x ∈ D, P (x)) ∧ (∀x ∈ D, Q(x)) ∀x ∈ D, (P (x) ∨ Q(x)), and (∀x ∈ D, P (x)) ∨ (∀x ∈ D, Q(x))

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A: Introduction :

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A: Proved the given consequent in natural deduction

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Q: 1. Construct a detailed truth table for the following propositional statement:  (((P ∨Q)∧¬P)→Q)…

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Q: Let P(x) and Q(x) be predicates and suppose D is the domain of x. For the statement forms in the…

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Q: Simplify the following assertions (so that ¬ does not appear).

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A: Answer: I have explained in brief. you ca see below in details.

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Q: 6)For each of the following equivalences, determine if it is valid for all predicates P and Q. If…

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A: As per the answering guidelines solving the first question completely.

Q: B. Determine whether these pairs of statements are logically equivalent. Justify your answer. a)…

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Inference in AI

The inference is finding a conclusion or result based on any data, events, and any information. Usually, there will be a set of conditions and the conclusion is made, which satisfies all the given conditions are true. The conclusion is made according to the inference rules. Any artificial intelligence agent or an intelligent system uses the inference engine to find a better result or output. The work of the inference engine is to analyze the fact and figures based on all circumstances. After the analysis, the machine concludes this fact and gives it to the agent. The agent uses this conclusion for further processing and decision-making. Intelligent systems will generate new logic from existing ones based on the facts.