# Proof;

To prove **cl(A∩B) ⊆ cl(A)∩cl(B)**, where A and B are Subsets of X, we have need to show that (A∩B) ⊆ cl(A) ∩ cl(B) at first and then cl(A∩B) ⊆ cl(A) ∩ cl(B) .

Prove that if A and B are Subsets of a topological Space (X, T) then cl(A∩B) ⊆ cl(A)∩cl(B). |

We know that **A ⊆ cl(A) and B ⊆ cl(B)**.

⇒ (A ∩ B) ⊆ cl(A) and (A∩B) ⊆ cl(B)

⇒ (A ∩ B) ⊆ cl(A) ∩ cl(B)

⇒ cl(A ∩ B) ⊆ cl(A) ∩ cl(B)

∵ cl(A) ∩ cl(B) is closed super set of (A ∩ B) and cl(A ∩ B) is the smallest closed super set of (A ∩ B)

**Hence proved that cl(A ∩ B) ⊆ cl(A) ∩ cl(B), where A and B are Subsets of topological Space (X, T).**