An electrochemical cell has the following standard cell notation.

mg(s) | mg^2+ (aq) || aq^+(aq) | aq(s)

write the balanced oxidation and reduction half reactions, labeling the oxidation reaction and the reduction reaction.

Explanation:

The given following standard cell notation.  

Mg(s) | Mg^2+ (aq) || Aq^+(aq) | Aq(s)

Oxidation:

....(1)

Magnesium metal by loosing 2 electrons is getting converted into magnesium cation. Hence, getting oxidized

Reduction:

...(2)

Silver ion by gaining 1 electrons is getting converted into silver metal. Hence, getting reduced.

Overall redox reaction: (1)+2 × (2)