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I'm reading a book on sets and it mentions a set B = {1,2,3,4}

and it says that

R3 = {(x, y) : x ∈ B ∧y ∈ B}

What does that mean? Does that mean every possible combination in the set?

Also the book doesn't clarify this completely but for example using the set B say i had another set

R = {(1,2),(2,3),(1,3),(1,1),(2,2),(3,3),(4,4)},

Would this be clarified as transitive and reflexive? My question is does a set need to have all transitive properties and all the reflexive properties to be called transitive and reflexive.

If i had another set:

R1 = {(1,2),(2,3),(1,3),(1,1),(2,2),(3,3)}

In which i removed (4,4) would this set R1 still be considered reflexive?

Thanks in advance

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# Equivalence Relations

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