“A set A” would be a collection of things (things are called elements of A)
You would express this as: $ x \in A $ - which means x is an element of A
$ \mathbb{N} = \lbrace 1, 2, 3, … ,\infty \rbrace = $ Set of All natural numbers
$ \mathbb{Z} = \lbrace 0, \pm 1, \pm 2, \pm 3, … ,\pm \infty \rbrace = $ Set of All Integers
$ \mathbb{Q} = \lbrace \dfrac {a} {b} \text{ } \vert \text{ } a, b \text{ } \in \mathbb{Z}, b \neq 0 \rbrace = $ Set of All Rational numbers; all numbers that can be expressed as a number above another number
$ \mathbb{R} = $ Real; any number that can be expressed in any way
$ \cup $ is called a “cup” or “union” and it is used to refer to the area of sets together
$ A \cup B = \lbrace x \in A \text{ } or \text{ } x \in B \rbrace $
$ \cap $ is called a “cap” or “intersection” and its used to refer to the overlap of sets
$ A \cap B = \lbrace x \in A \text{ } and \text{ } x \in B \rbrace $
$ \subset $ is called a set inclusion and it signifies that one set (the set on the closed end) is inside another set (the set on the open end)
$ A \subset B = \lbrace x \in A \text{ } \rightarrow \text{ } x \in B \rbrace $
$ \diagdown $ refers to a set that is in the first set but not in the second
$ A \diagdown B = \lbrace x \in A \text{ } but \text{ } x \in B \rbrace $