(* ::Package:: *)

addParan[g_]:=Module[{e},

e=EdgeList@g;

e=DeleteDuplicates[(Flatten@Table[{e[[i]][[1]]\[DirectedEdge]e[[i]][[2]], e[[i]][[2]]\[DirectedEdge]e[[i]][[1]]},{i,1,Length@e}])~Join~EdgeList[g, _\[DirectedEdge]_]];
Table["("<>StringReplace[ToString@e[[i]],{"\[DirectedEdge]"->","}]<>")",{i, 1, Length@e}]

];





notRelation[]:=Module[{list},

list=RandomSample[Tuples[Range@10,2],5]~Join~RandomSample[Tuples[Range@10,3],RandomInteger[{1,2}]]~Join~RandomSample[Tuples[Range@10,1],RandomInteger[{1,2}]];

list=RandomSample[list,Length@list];

<|
"tuples"->Table[StringReplace[ToString[list[[i]]],{"{"->"(","}"->")"}],{i,1,Length@list}]

|>

];



makeRelation[]:=Module[{mod,suffixQ,g,stringLIST,size=300},
stringLIST={{"d","cd","bcd","abcd"},{"AA","BAACGF","A","AB","AC","CGF"},{"draw","drawing","drawn","drew"}};
<|


"symmetricNOT"->RandomChoice@{

<|
g=RelationGraph[Less,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a<b ", TraditionalForm]
|>

,


<|
g=RelationGraph[Greater,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a>b ", TraditionalForm]
|>

},

"symmetric"->RandomChoice@{

<|
g=RelationGraph[Unequal,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[NotEqual]b ", TraditionalForm]
|>
,

<|
mod[s1_,s2_]:=Mod[s1-s2,2]===0;
g=RelationGraph[mod,Range[RandomInteger[{4,5}]],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[Congruent]b (mod 2)", TraditionalForm]


|>

},

"reflexiveNOT"->RandomChoice@{

<|
g=RelationGraph[Less,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a<b ", TraditionalForm]
|>

,


<|
g=RelationGraph[Greater,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a>b ", TraditionalForm]
|>

,

<|
g=RelationGraph[Unequal,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[NotEqual]b ", TraditionalForm]
|>


},


"reflexive"->RandomChoice@{

<|

g=RelationGraph[StringContainsQ,RandomChoice@stringLIST ,DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] b sub-string in a", TraditionalForm]


|>,

<|
g=RelationGraph[LessEqual,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[LessSlantEqual]b ", TraditionalForm]
|>
,
<|
mod[s1_,s2_]:=Mod[s1-s2,2]===0;
g=RelationGraph[mod,Range[RandomInteger[{4,5}]],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[Congruent]b (mod 2)", TraditionalForm]


|>

},


"equivalenceNOT"->RandomChoice@{

<|

g=RelationGraph[StringContainsQ,RandomChoice@stringLIST ,DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] b sub-string in a", TraditionalForm]


|>,

<|
g=RelationGraph[Unequal,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[NotEqual]b ", TraditionalForm]
|>
,
<|
g=RelationGraph[Less,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a<b ", TraditionalForm]
|>



}
,

"equivalence"->RandomChoice@{

<|
g=RelationGraph[LessEqual,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[LessSlantEqual]b ", TraditionalForm]
|>
,

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a identical to be b", TraditionalForm]

|>,

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a same age as b", TraditionalForm]

|>,

<|
mod[s1_,s2_]:=Mod[s1-s2,2]===0;
g=RelationGraph[mod,Range[RandomInteger[{4,5}]],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[Congruent]b (mod 2)", TraditionalForm]


|>,

<|
g=RelationGraph[Equal,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a=b ", TraditionalForm]
|>


},


"transitiveNOT"->RandomChoice@{

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a daughter of b", TraditionalForm]

|>

,

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a sister of b", TraditionalForm]

|>

,

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a feeds on b", TraditionalForm]

|>

,

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a likes b", TraditionalForm]

|>
,

<|

"graph"->Nothing,
"relation"->Nothing,
"tuples"->Nothing,
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a hates b", TraditionalForm]

|>


},


"transitive"->RandomChoice@{

<|

g=RelationGraph[StringContainsQ,RandomChoice@stringLIST,DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] b sub-string in a", TraditionalForm]


|>,

<|
g=RelationGraph[Unequal,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[NotEqual]b ", TraditionalForm]
|>
,
<|
mod[s1_,s2_]:=Mod[s1-s2,2]===0;
g=RelationGraph[mod,Range[RandomInteger[{4,5}]],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}],
"tuples"->addParan[g],
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[Congruent]b (mod 2)", TraditionalForm]


|>
,

<|
g=RelationGraph[LessEqual,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*),
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a\[LessSlantEqual]b ", TraditionalForm]
|>
,

<|
g=RelationGraph[Less,RandomSample[Range[-9,9],4],DirectedEdges->True,VertexLabels->"Name",ImageSize->size];
"graph"->g,
"relation"->Nothing(*StringReplace[ToString[EdgeList@g,TraditionalForm],{"\[DirectedEdge]"->"\[ScriptCapitalR]", "\[UndirectedEdge]"->"\[ScriptCapitalR]"}]*),
"tuples"->Nothing(*addParan[g]*), 
"definition"->ToString["a\[ScriptCapitalR]b \[DoubleLongLeftRightArrow] a<b ", TraditionalForm]
|>
}
|>




];