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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You know that $\displaystyle ~(a,b) \in R \circ (S \cap T)\; \Rightarrow \;\left( {\exists c} \right)\left[ {(a,c) \in (S \cap T) \wedge (c,b) \in R} \right]$. Can you finish?
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?
Originally Posted by rnuravvk 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 $\displaystyle (a,c) \in S \wedge (c,b) \in R\;\& \,(a,c) \in T \wedge (c,b) \in R$. What does that imply?
That the composition of S with T and T with R are intersecting one another?
Originally Posted by rnuravvk 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.
So I re-thought it over and think this is it. The pair (a,b) is an element of S,T and R
Originally Posted by rnuravvk 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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