Associative Property of intersection of sets A ∩ (B ∩ C) = (A ∩ B) ∩ C

B ∩ C = ${\displaystyle \{\sqrt{3},\sqrt{5},6,13\}\cap \{\sqrt{2},\sqrt{3},\sqrt{5},9\}=\{\sqrt{3},\sqrt{5}\}}$

 A ∩ (B ∩ C) = ${\displaystyle \{-11,\sqrt{2},\sqrt{5},7\}\cap \{\sqrt{3},\sqrt{5}\}=\left\{\sqrt{5}\right\}}$  ...(1)

A ∩ B  = ${\displaystyle \{-11,\sqrt{2},\sqrt{5},7\}\cap \{\sqrt{3},\sqrt{5},6,13\}=\left\{\sqrt{5}\right\}}$

(A ∩ B) ∩ C = ${\displaystyle \left\{\sqrt{5}\right\}\cap \{\sqrt{2},\sqrt{3},\sqrt{5},9\}=\left\{\sqrt{5}\right\}}$  ...(2)

From (1) and (2),

It is verified that A ∩ (B ∩ C) = (A ∩ B) ∩ C