Question

Let be a function with domain X and range Y. Let A, B $⊑$ X and C, D $⊑$ Y. Which of the following is not true?

• A. $f(A\cup B)=f\left(A\right)\cup f\left(B\right)$
• B. $f(A\cap B)=f\left(A\right)\cap f\left(B\right)$
• C. $f^1(C\cup D)=f^1\left(c\right)\cup f^{-1}\left(D\right)$
• D. $f^1(C\cap D)=f^1\left(c\right)\cap f^{-1}\left(D\right)$

Answer 1

The correct option is B $f(A\cap B)=f\left(A\right)\cap f\left(B\right)$

Since, $f\left(A\right)\cap f\left(B\right)⊑f(A\cap B)$ may not be true.