4 proof Questions , Please Help

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4 proof Questions , Please Help

Postby zack95 » Tue May 27, 2014 9:13 am

I have exam next week and Need to know the answer of thease questions that I can not answer to them.
So, if it is possible , please help me. :confused:
Thank you

Question 1) Proof that def1 and def2 are equal. ( using convex fuzzy sets.) (Question 1 is Fuzzy sets Question)
def1= Fuzzy sets is convex iff For all of x, 0<x<=1 , x-cut is convex.
def2= x1 <= For all of x <= x2 , Membership function(x) >= minimum( Membership function(x1) , Membership function(x2) )

Question 2) A is a subset of X and B is a subset of Y : (Question 2 is Function Question)
1)proof that A is a subset of f-inverse(f(A))
2)proof that B is a superset of f(f-inverse(B))

Question 3) A=[1,4] , B=[7,10]
proof that A+B={for C member of R|C=a+b , For all a member of A , For all b member of B}=[8,14]

Question 4)(function Question) If f: x --> y , g: y --> z and f,g are Bijection(Bijection means One-to-One and Onto at a same time)
proof that gof is Bijection.
note that gof means g(f(x)). (Question 4 is function Question)

I have problem with these proof.
Please help me.
Thank you :clap:

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Postby stapel_eliz » Tue May 27, 2014 11:13 am

These are graduate-level questions. Please reply with your efforts so far, including the definitions and the theorems which you are applying to each proof. Thank you.

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