Question

Part II
True or false:

a. A surjective function defined in a finite set X over the same set X is also BIJECTIVE.

b. All surjective functions are also injective functions

c. The relation R = {(a, a), (e, e), (i, i), (o, o), (u, u)} is a function of V in V if
V = {a, e, i, o, u}.

d. The relation in which each student is assigned their age is a function.

e. A bijective function defined in a finite set X on the same set X is also surjective. 

f.  A bijective function defined in a finite set X on the same set X cannot be surjective.

g.  An surjective function defined in a finite set X on the same set X is also injective.

Answer 1

a) True, because over finite set if function is injective or surjective then the function is bijective

b) False, because f is function from {1,2,3} to {1,2} and defined as f(1)=f(2)=1 and f(3)=2 then map is surjective but f is not injective

c)True, because R is a identity function on a set A which assigns element to a unique element in A

d)True, since every student has unique age so unique image so it is a function

e)True, because bijective functions both injective and surjective

f)False ,

g)True, since same reason as in part a)