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Thread: Equality Relation

  1. #1
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    Equality Relation

    Hi, I was having some trouble with this problem:

    Show the equality relation = on M as a set of tuples of the appropriate length. Where Mis the numbers {0,1,2}. I know to prove equality, you must prove it is reflexive, symmetric, and transitive. However, I'm unsure on how to do this with tuples. Any help is appreciated, thank you so much!
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  2. #2
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    Re: Equality Relation

    Quote Originally Posted by STEMSTRUGGLES View Post
    Hi, I was having some trouble with this problem:
    Show the equality relation = on M as a set of tuples of the appropriate length. Where Mis the numbers {0,1,2}. I know to prove equality, you must prove it is reflexive, symmetric, and transitive. However, I'm unsure on how to do this with tuples. Any help is appreciated, thank you so much!
    The minimal equivalence relation is $\{(0,0),(1,1),(2,2)\}$. That is equality.
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    Re: Equality Relation

    Quote Originally Posted by Plato View Post
    The minimal equivalence relation is $\{(0,0),(1,1),(2,2)\}$. That is equality.
    Hey Plato,

    Thank you for the quick response! You said the answer was $\{(0,0),(1,1),(2,2)\}$, but would I also need $(0,1), (1,2), (0,2)$ to prove transitivity? Thanks!
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    Re: Equality Relation

    Quote Originally Posted by STEMSTRUGGLES View Post
    Hey Plato,

    Thank you for the quick response! You said the answer was $\{(0,0),(1,1),(2,2)\}$, but would I also need $(0,1), (1,2), (0,2)$ to prove transitivity? Thanks!
    Tell us why you think those pairs are necessary.
    Because if you think they are then you do not understand transitivity.
    The diagonal relation, $\Delta_A=\{(x,x) : x\in A\}$, is the equality relation on $A$.
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