(Discrete Math-Graph Theory) Let G=(V,E₁∪E₂∪E₃) be a simple graph such that G₁=(V,E₁) is planar, G₂=(V,E₂) is a forest, and G₃=(V,E₃) is a matching. Prove G is 9-colourable, i.e. its chromatic number satisfies χ(G)≤9.

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