Consider a function 3 from set X to set X. Suppose that X = A U...

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Consider a function 3 from set X₁ to set X₂. Suppose that X₁ = A₁ U A₂ with A₁ and A2 being disjoint. Prove or disprove the following claim: If the restrictions 3 A, i = 1, 2, are injective, then 3 is injective. Consider a function 3 from set X₁ to set X₂. Suppose that X₁ = A₁ U A₂ with A₁ and A2 being disjoint. Prove or disprove the following claim: If the restrictions 3 A, i = 1, 2, are injective, then 3 is injective.