Question

Give a model of the sentence

$$\begin{gathered} {\phi }_{I{t}_{}}=\wedge {\forall }_{X,Y}{[R_1(x,x)]}_{} \\ \wedge \forall x.y\left[R_1\right(x,y)\to (R_1(y,x)] \\ \wedge {\forall }_{x,y,z}[\left(R_1\right(x,y)\wedge R_1(y,z\left)\right)\to R_1(x,z)] \end{gathered}$$

Short answer

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 ${\phi }_{eq}$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 ${\phi }_{eq}$

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, ${\phi }_{eq}$will be satisfied by (A,$R_{1)..}$