Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist. i. A= v,w,x,y,z, B=1,2,3,4,5 R= (v,z),(w,1), (x,3),(y,5) ii. A = 1,2,3,4,5 B=1,2,3,4,5 R = (1,2),(2,3),(3,4),(4,5),(5,1)
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We know that a function is called injective if the values of the function are equal if and only when the arguments are equal .
The function is called subjective if For each element of the set B, there is its inverse image with respect to the function: .
i.In this case is not a function acting from set t the set , becuse in . It is not a function at all, s it can't be injective and/or subjective.
ii. In this case for all values of the function there exist different arguments from the set . So the function is injective. equals , so the function is subjective. The universe of the function is
The inverse function to the function is .