question_answer

Let R f be a function with domain X and range Y. Let \[A,\text{ }B\text{ }\subseteq X\]and \[C,\text{ }D\text{ }\subseteq \text{ Y}\]. Which of the following is not true?

A)  \[f(A\cup B)=f(A)\cup f(B)\]

B)  \[f(A\cap B)=f(A)\cap f(B)\]

C)  \[{{f}^{-1}}(C\cup D)={{f}^{-1}}(C)\cup {{f}^{-1}}(D)\]

D)  \[{{f}^{-1}}(C\,\cap D)={{f}^{-1}}(C)\cap {{f}^{-1}}(D)\]