What do these operations mean? $A ∩ B$ or $ A ∪ B$ or $A^c$?

Question

To be more specific; What does it mean when I read my book:

$A ∩ B = (2, 4) $ ? What does this say about A and B? How are they related?

Same with:
$A ∪ B $

and,

$A^c$ , where c is a complement operator??

Answer 1

$A \cap B$ is the intersection of $A$ and $B$. It's the set of all elements that are in both $A$ and $B$.

For example, if $A = [0, 4)$ and $B = (2,5]$, then $A \cap B = (2,4)$.

$A \cup B$ is the union of $A$ and $B$. It's the set of all elements that are in $A$, or in $B$, or in both.

For example, if $A = [0, 4)$ and $B = (2,5]$, then $A \cup B = [0,5]$.

$A^c$ is the complement of $A$. To make sense of complement you need to know what your universal set is. $A^c$ is the set of everything in the universal set that is not in $A$.

For example, if the universal set is $[0,10]$, and $A = [0,3]$, then $A^c = (3,10]$.