Answer to Question #185753 in Discrete Mathematics for zain ul abdeen

Question

Let f be a function from the set A to the set B. Let S and T be two disjoint subsets of A (i.e S∩T=∅); then which of the following cannot be true: 

a) if f is invertible, then f(S)∩f(T)=∅   

b) if f(S)∩f(T)≠∅, then f is a one-to-one function

c) if f(S)∪f(T)⊆B, then f is an onto function

d) none of the above

Answer 1

$f:A\rightarrow B$

$S,T \subset A, (S\cap T)=\phi$

Option (c) is not true, Because if f(S)∪f(T)⊆B, Then fis not an onto function, As Set B is the union of these two function, So f is not an onto function.