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Math Help - Proof

  1. #1
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    Proof

    Prove the Following:

    R ◦ (S ∩ T) ⊆ (R ◦ S) ∩ (R ◦ T)

    I think this is trying to show that this proof is trying to show that the compositions of relations are associative.
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  2. #2
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    You know that ~(a,b) \in R \circ (S \cap T)\; \Rightarrow \;\left( {\exists c} \right)\left[ {(a,c) \in (S \cap T) \wedge (c,b) \in R} \right].

    Can you finish?
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  3. #3
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    Can we say that since the pair (c,b) is an element of R and the pair (a,c) is an element of (S ∩ T) then the pair (a,c) is an element of both?
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  4. #4
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    Quote Originally Posted by rnuravvk View Post
    Can we say that since the pair (c,b) is an element of R and the pair (a,c) is an element of (S ∩ T) then the pair (a,c) is an element of both?
    So (a,c) \in S \wedge (c,b) \in R\;\& \,(a,c) \in T \wedge (c,b) \in R. What does that imply?
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  5. #5
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    That the composition of S with T and T with R are intersecting one another?
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  6. #6
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    Quote Originally Posted by rnuravvk View Post
    That the composition of S with T and T with R are intersecting one another?
    I must ask you: "Do you understand any of this"?
    Are you just making wild guesses?
    If not, please give some reasons.
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  7. #7
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    So I re-thought it over and think this is it. The pair (a,b) is an element of S,T and R
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  8. #8
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    Quote Originally Posted by rnuravvk View Post
    So I re-thought it over and think this is it. The pair (a,b) is an element of S,T and R
    You are guessing are you not?
    Where are the compositions?
    Do you understand what any of this means?
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