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August 19th, 2017, 04:38 PM  #1 
Newbie Joined: Aug 2017 From: mathmatistan Posts: 9 Thanks: 0  several questions about relations and functions
Hello, I'm having trouble with the concept of relations and functions. I don't understand some concepts and I'd like your help to do that if you can. Let's say we have a simple set M that is the relation set of A={1,2,3}. a) the number of elements of M? Is it 1M3,1M2,2M1,2M3,3M1,3M2,3M1 or do you not count the "opposites", like 1M3,3M1? Let's say that s:m>m is the function that assigns for every $\displaystyle R \in M$ its symmetrical complement (I don't know the term in English, so I'll provide the mathematical definition: $R \cup R^{1} = R \cup \{\langle a,b\rangle\,\,\langle b,a\rangle \in R\}$). b) is M injective? It seems that not since every element in the domain has more than one link in the range. (x doesn't have a unique y), how do I write it mathematically? c) is M surjective? Every value of f(x) seems to have at least one value of x. d) for every [MAT]R1,R2 \in M[/MATH] is $\displaystyle s(R_1 R_2)=s(R_1)s(R_2)$ (relation multipication) seems to be true. since if we have {<1M3>,<1M2>,<2M1>,<2M3>,<3M1>,<3M2>,<3M1>}, after assigning the multiplication through function s (as explained, s is defined s:m>m and assigns its symmetrical complement), as since we don't write each element twice, it holds. is it okay to write that as a proof? e) for every $\displaystyle R \in M$, $\displaystyle s(s(R))=s(R)$ seems to be very trivial, since you assign the complement and then assign the complement of it, it's like $\displaystyle (x^{1})^{1}$ or don't I understand it correctly? If you can, please help me with this as it's very important for a test I'll have on Monday. I've elaborated and explained my thoughts, so please correct me if I'm mistaken. Thank you in advance! Last edited by skipjack; August 19th, 2017 at 06:51 PM. 
August 23rd, 2017, 05:00 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896  Quote:
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functions, injective, questions, relation, relations, settheory, surjective 
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