For each of the following sets, a) S={1,2,3}, T ={a, b, c} b) S={a, b}, T ={1,2,3,4} c) S={1,2,3,4}, T ={a, b} Determine whether 1. There is a one-to-one function f:S→T; 2. There is an onto function f:S→T; and 3. If there is a bijective function f:S→T. 4. For each (1–3) if such a function exists, explicitly give it. If no function exists give a short explanation?
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- f : S→T - one-to-one function
a) f(1) = a
f(2) = b
f(3) = c
b) f(a) = 1
f(b) = 2
c) There isn't a one-to-one function, because S has more elements than T.
2.f : S→T - onto function
a) f(1) = a
f(2) = b
f(3) = c
b) There isn't a onto function, because S has less elements than T.
c) f(1) = a
f(2) = a
f(3) = b
f(4) = b
3.f : S→T - bijective function
a) f(1) = a
f(2) = b
f(3) = c
b) and c) There isn't bijective function, because S and T have different numbers of elements.