Concept:
The oxidation state of an element is the apparent charge assigned to it in a compound according to the oxidation number rules.
Some important rules are:
• Fluorine always has oxidation state \(-1\).
• The oxidation state of an element in its free state is \(0\).
• The algebraic sum of oxidation states of all atoms in a neutral molecule is zero.
Since fluorine is the most electronegative element, oxygen exhibits a positive oxidation state in compounds containing fluorine.
Step 1: Find the oxidation state of oxygen in \(O_{2}F_{2}\).
Let the oxidation state of oxygen be \(x\).
Since fluorine has oxidation state \(-1\),
\[
2x+2(-1)=0.
\]
Therefore,
\[
2x-2=0,
\]
\[
2x=2,
\]
\[
x=+1.
\]
Hence,
\[
\boxed{\text{Oxidation state of oxygen in }O_{2}F_{2}=+1.}
\]
Step 2: Find the oxidation state of oxygen in \(O_{3}\).
Ozone is an allotrope of oxygen.
Since it exists in the elemental state,
\[
\boxed{\text{Oxidation state of oxygen}=0.}
\]
Step 3: Identify the correct option.
Thus,
\[
O_{2}F_{2}\rightarrow +1,
\]
\[
O_{3}\rightarrow 0.
\]
Hence,
\[
\boxed{\textbf{Option (A)}}
\]
is the correct answer.