The element that does not show positive oxidation state is:
(i) \[O\]
(ii) $N$
(iii) $F$
(iv) $Cl$

Hint: For an element to show positive oxidation state, the element must be bonded to a more electronegative element so that the more electronegative atom acquires negative oxidation state while the element acquires positive oxidation state. Find out the element which fulfills this criteria.

Complete step-by-step answer:
Oxidation state indicates the degree of oxidation for an atom in a chemical compound. It is the hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic. Oxidation states are typically represented by integers, which can be positive, negative, or zero.
For an element to show positive oxidation state, the element must be bonded to a more electronegative element so that the more electronegative atom acquires negative oxidation state while the element acquires positive oxidation state.
The given elements are $O,\,N,\,F,\,Cl$.
\[O\] usually shows oxidation state of $\left( { - 2} \right)$ but in compounds with $F$it shows a positive oxidation state. Example: ${O_2}{F_2}$ where \[O\] has an oxidation state of $\left( { + 1} \right)$.
The oxidation state of \[N\] can encompass from an oxidation state of $\left( { - 3} \right)$to an oxidation state of $\left( { + 5} \right)$ hence can show positive oxidation state. Example: $N{O_2}$ where \[N\] has an oxidation state of $\left( { + 4} \right)$.
\[Cl\] usually shows oxidation state of $\left( { - 1} \right)$ but in compounds with $F$ and $O$ it shows a positive oxidation state. Example: $HCl{O_4}$ where \[Cl\] has an oxidation state of $\left( { + 7} \right)$.
But $F$ is the most electronegative element present in the periodic table and hence cannot show positive oxidation state when combined with any other element of the periodic table.
Hence $F$ do not show positive oxidation state.

So the correct answer is (iii) $F$.

Note:For this question you must have a good knowledge of the placement of a particular element in the periodic table as the position of the element in the periodic table determines the oxidation states that can be shown by the given element. Also remember $F$ cannot show positive oxidation state under any condition.