According to the official health claims of the European Food Safety Authority (EFSA):
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Zinc:
Contributes to the normal function of the immune system.
Contributes to the protection of cells from oxidative stress.
Contributes to the maintenance of normal hair, nails and skin.
Contributes to normal DNA and protein synthesis.
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Vitamin C:
Contributes to the normal function of the immune system.
Contributes to the protection of cells from oxidative stress.
Contributes to the reduction of tiredness and fatigue.
Contributes to normal energy-yielding metabolism.