An independent set in a graph G = (V, E) is a set I ⊆ V with the following property:
∀u ∈ I. ∀v ∈ I. {u, v} ∉ E.
This question explores independent sets and their properties.

Prove or disprove: if G = (V, E) is a graph and I₁ and I₂ are independent sets in G, then I₁ ∩ I₂ is
an independent set in G.
Independent sets are specified using a definition given in first-order logic. Make sure your proof is structured around that definition, the same way that proofs of reflexivity, symmetry, etc. are structured around those first-order definitions.