Formalize the following argument by using the given predicates and then rewriting the argument as a numbered sequence of statements. Identify each statement as either a premise, or a conclusion that follows according to a rule of inference from previous statements. In that case, state the rule of inference and refer by number to the previous statements that the rule of inference used. Dogs bark at cats. Max is a dog. Moonbeam is a cat. Therefore, Max barks at Moonbeam. Predicates: B(x,y) = "x barks at y". D(x) = "x is a dog". C(x) ="x is a cat". The common domain of discourse is all animals.

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01-10-2020
Mathematics

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Formalize the following argument by using the given predicates and then rewriting the argument as a numbered sequence of statements. Identify each statement as either a premise, or a conclusion that follows according to a rule of inference from previous statements. In that case, state the rule of inference and refer by number to the previous statements that the rule of inference used. Dogs bark at cats. Max is a dog. Moonbeam is a cat. Therefore, Max barks at Moonbeam. Predicates: B(x,y) = "x barks at y". D(x) = "x is a dog". C(x) ="x is a cat". The common domain of discourse is all animals.

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codiepienagoya codiepienagoya · Answer 1 · 2020-10-02T06:55:29+02:00

Answer:

The answer is "[tex]\bold{((P_2 \wedge P_3)\longrightarrow P_1 \longrightarrow P_1 }[/tex]".

Step-by-step explanation:

Let assuming the following predicates:

[tex]\to B(x,y)= \text{x barks at y} \\\\\to D (x)= \text{x is a dog} \\\\\to C (x)= \text{x is a cat} \\\\[/tex]

In the given table it calculates the numbered sequence, which is given in the statement and calculates the other details, please find the attached file.

Premise P1 means whether dogs are shouting at cats.

Premise P2 means Maximum is a dog.

Premise P3 means that a cat is Moonbeam.

Unless the assumptions P1, P2, and P3 all are valid, otherwise the conclusion that Maximum starts barking at Moonbeam also is correct.

By both the law of deduction of Modus Ponens, statement 4 is the interpretation of states 1, 2, and 3. That conclusion can thus be conveyed as follows:

so, the final answer is "[tex]\bold{((P_2 \wedge P_3)\longrightarrow P_1 \longrightarrow P_1 }[/tex]"