The Boolean Logic of Set Intersections

$A \cap A = A$

$A \cap \mathbb{N} = \{1, 4, 27\}$ (Remember, $\mathbb{N}$ is the set of natural numbers.)

$A \cap \mathbb{R} = \varnothing$ (Remember, $\mathbb{R}$ is the set of real numbers.)

$A \cap \varnothing = A$

For any set $B$, $A \cap B = B \cap A$

For any sets $B$ and $C$, $A \cap (B \cap C) = (A \cap B) \cap C$

For any set $B$, $A \cap B \not= B$