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Math Help - Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show that

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    Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show that

    Suppose that A, B, C and D are sets, R is a relation between A and B
    (i.e., R ⊆ A x B), S is a relation between B and C and T is a relation
    between C and D. Show the following:
    (a) R (S T) = (R S) T.
    (b) (R S)⁻ = S⁻ R⁻ .

    Please help
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    Re: Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show

    Quote Originally Posted by habsfan31 View Post
    Suppose that A, B, C and D are sets, R is a relation between A and B
    (i.e., R ⊆ A x B), S is a relation between B and C and T is a relation
    between C and D. Show the following:
    (a) R (S T) = (R S) T.
    (b) (R S)⁻ = S⁻ R⁻ .
    Cannot help if you don't tell about notation.
    Does "R S" mean composition"
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    Re: Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show

    Yup, sorry bout that
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    Re: Math Logic: Let A, B, C and D be sets, and R ⊆ A x B, S ⊆ B x C, T ⊆ C x D. Show

    Quote Originally Posted by habsfan31 View Post
    Yup, sorry bout that
    If think then you have it backwards.
    S\circ R exists but R\circ S does not.
    Because R relates A\to B and S relates B\to C.
    So it must be S\circ R.
    Unless your text material is completely non-standard.
    It is usual for compositions to read right to left.


    Post Script
    Do you understand what I have posted?
    If {\mathcal{G}}\subseteq (U\times V)~\&~ {\mathcal{H}}\subseteq (V\times W) then if U\ne W then \mathcal{H}\circ \mathcal{G}
    exists BUT \mathcal{G}\circ \mathcal{H} may not.

    By definition (u,w)\in \mathcal{H}\circ \mathcal{G} \iff \left( \exists v \right)[(u,v)\in \mathcal{G}~\&~(v,w)\in \mathcal{H}].

    That means that \text{Dom}(\mathcal{H})\subseteq\text{Img}(\mathca  l{G}).
    Last edited by Plato; September 19th 2011 at 03:08 PM.
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