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If a substance gains oxygen during a reaction, it is being oxidized. If it loses oxygen, it is being reduced. Oxidation and reduction always take place together, so that If one substance is oxidized, another is reduced. Using this idea, say which substance is oxidized and which substance is reduced in each reaction.
1. ${\text{2Mg + }}{{\text{O}}_2} \to {\text{ 2MgO}}$
2. ${\text{ZnO + C}} \to {\text{ Zn + C}}{{\text{O}}_{}}$
3. ${\text{F}}{{\text{e}}_2}{{\text{O}}_3}{\text{ + CO}} \to {\text{ 2Fe + 3C}}{{\text{O}}_2}$
4. ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}{\text{ + 2Al}} \to {\text{ 2Cr + A}}{{\text{l}}_2}{{\text{O}}_3}$

Answer
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Hint: The question clearly states that oxidation is the addition of oxygen and removal of oxygen as a reduction. Therefore, carefully notice the number of oxygen attached to a molecule/compound before and after the chemical reaction.

Complete step by step solution:
1. In the first reaction, Mg ( Magnesium) is changing into Magnesium oxide. I.e., adding up of Oxygen hence oxidation.
${\text{2Mg + }}{{\text{O}}_2} \to {\text{ 2MgO}}$
If Magnesium ( ${\text{Mg}}$) is undergoing oxidation then Oxygen (${{\text{O}}_2}$) will undergo reduction.

2. ${\text{ZnO + C}} \to {\text{ Zn + C}}{{\text{O}}_{}}$
In this reaction Zinc oxide (${\text{ZnO}}$) is converted into zinc (${\text{Zn}}$, decreased number of oxygen) and carbon is converted into carbon monoxide (${\text{C}}{{\text{O}}_{}}$, increased number of oxygen),
Therefore, carbon is undergoing oxidation, and zinc oxide (${\text{ZnO }}$) is undergoing reduction

3. ${\text{F}}{{\text{e}}_2}{{\text{O}}_3}{\text{ + CO}} \to {\text{ 2Fe + 3C}}{{\text{O}}_2}$
In this reaction of iron oxide (${\text{F}}{{\text{e}}_2}{{\text{O}}_3}$) with carbon monoxide (${\text{CO}}$) the product formed are Iron [${\text{Fe}}$, where Iron has lost oxygen] and Carbon dioxide [${\text{C}}{{\text{O}}_2}$, where carbon has more oxygen]. Hence it is evident that iron oxide ${\text{F}}{{\text{e}}_2}{{\text{O}}_3}$ is undergoing reduction and carbon monoxide (${\text{CO}}$) is undergoing oxidation.

4. ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}{\text{ + 2Al}} \to {\text{ 2Cr + A}}{{\text{l}}_2}{{\text{O}}_3}$
This last reaction involves the formation of chromium (${\text{Cr}}$) and Aluminium oxide (${\text{A}}{{\text{l}}_2}{{\text{O}}_3}$), from Chromium oxide (${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$) and Aluminium (${\text{Al}}$), therefore, it is clear
that ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$is undergoing reduction (losing oxygen) and Aluminium is undergoing oxidation (gaining oxygen).

Note: If you're confused with oxidation and reduction in general try to remember it by the concepts of oxygen and oxidation number, if there is an increase in both then it is oxidation and reduction is just the opposite of oxidation.