The following predicate logic formulas is invalid: Vx, 3y.P(x,y) = 3y, Vx.P(x, y) Indicate which of the following are counter models for this formula and briefly explain your reasoning. 1. The predicate P(x,y) ::= y+x = 1 where the domain of discourse is N. 2. The predicate P(x,y) ::= y·x = 2 where the domain of discourse is R without 0. 3. The predicate P(x,y)::= yxy = x where the domain of discourse is the set of all binary strings, including the empty string 2.

Q: What is the relevance of Boolean algebra for computer scientists?

A: Boolean algebra is a branch of mathematics that deals with the operations on logical values with…

Q: Please elaborate on the many applications of Automata Theory.

A: The answer is given below step.

Q: What is the truth table for PŹ q nC.

A: Refer to step 2 for the answer.

Q: Why is it important for computer scientists to grasp Boolean algebra?

A: The Basics of Boolean Algebra: Conjunction, disjunction, and negation are the three fundamental…

Q: Why is it crucial for programmers to understand Boolean algebra?

A: The following are some examples of the importance of Boolean algebra to computer scientists: In the…

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.