13. Is the following proposition true or false? Justify your conclusion with a proof or a
counterexample. If f : S arrow T is a surjection and C subset of T, then f (f^-1 (C)) = C.
Solution
If f:S to T is a surjection, then
all elements in T = f(C)
Hence each element in f(C) has a preimage in C
But as f is not one to one, the preimage is not unique.
Hence there may be repititions.
f inverse is not a funciton. We can say f inverse is a mapping for a mapping f
f( f inverse C) =C
For a funciton f, the above is not true..
13. Is the following proposition true or false Justify your conclusi.pdf
1. 13. Is the following proposition true or false? Justify your conclusion with a proof or a
counterexample. If f : S arrow T is a surjection and C subset of T, then f (f^-1 (C)) = C.
Solution
If f:S to T is a surjection, then
all elements in T = f(C)
Hence each element in f(C) has a preimage in C
But as f is not one to one, the preimage is not unique.
Hence there may be repititions.
f inverse is not a funciton. We can say f inverse is a mapping for a mapping f
f( f inverse C) =C
For a funciton f, the above is not true.
