Question

Let $f:A\to B$ be a function, and let $E$ and $F$ be subsets of $A$. Consider the following statements about images.

$S_1:f(E\cup F)=f\left(E\right)\cup f\left(F\right)$
$S_2:f(E\cap F)=f\left(E\right)\cap f\left(F\right)$

• A. Only $S_1$ is correct
• B. Only $S_2$ is correct
• C. Both $S_1$ and $S_2$ are correct
• D. None of $S_1$ and $S_2$ is correct

Answer 1

The correct option is A Only $S_1$ is correct

Given a function $f:x\to y$ and subsets $E$ and $F$ of $A$ then we have
$f(E\cup F)=f\left(E\right)\cup f\left(F\right)$ and
$f(E\cap F)\subseteq f\left(E\right)\cap f\left(F\right)$
Therefore $S_1$ is correct and $S_2$ is false.