Chapter 6: Q10P (page 270)

Give a model of the sentence
$φ_{I t_{}} = \land \forall_{X, Y} {[R_{1} (x, x)]}_{} \land \forall x . y [R_{1} (x, y) \to (R_{1} (y, x)] \land \forall_{x, y, z} [(R_{1} (x, y) \land R_{1} (y, z)) \to R_{1} (x, z)]$

Short Answer

Expert verified

Answer:

The solution is given below.

Step by step solution

Turing Machine

A Turing Machine is computational model concept that runs on the unrestricted grammar of Type-zero. It accepts recursive enumerable language. It comprises of an infinite tape length where read and write operation can be perform accordingly.

proof.

The statement $φ_{e q}$ gives the three conditions of an equivalence relation.

WE can assume a model of the form ( A, $R_{1}$ )

Here, A will be a universal set and R₁ will be the equivalence relation on the element p $\in$ A.

This is correct model over $φ_{e q}$

For an example, if A is set of all integers Z and $R_{1}$ = {(i,j): i,j $\in$ Z}

Here, i and j can be equal or not. So, $φ_{e q}$ will be satisfied by (A, $R_{1) . .}$

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Give a model of the sentence
$φ_{I t_{}} = \land \forall_{X, Y} {[R_{1} (x, x)]}_{} \land \forall x . y [R_{1} (x, y) \to (R_{1} (y, x)] \land \forall_{x, y, z} [(R_{1} (x, y) \land R_{1} (y, z)) \to R_{1} (x, z)]$

Short Answer

Step by step solution

Turing Machine

proof.

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Give a model of the sentenceφIt=∧∀X,Y[R1(x,x)]∧∀x.y[R1(x,y)→(R1(y,x)]∧∀x,y,z[(R1(x,y)∧R1(y,z))→R1(x,z)]

Short Answer

Step by step solution

Turing Machine

proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

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Study anywhere. Anytime. Across all devices.

Give a model of the sentence
$φ_{I t_{}} = \land \forall_{X, Y} {[R_{1} (x, x)]}_{} \land \forall x . y [R_{1} (x, y) \to (R_{1} (y, x)] \land \forall_{x, y, z} [(R_{1} (x, y) \land R_{1} (y, z)) \to R_{1} (x, z)]$