Hi,

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.

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