Equal volumes of 0.1m naoh and 0.1m hcl are thoroughly mixed. the resulting solution has a ph closest to

Lets assume x volume of NaOH and x volume of HCl are added together.
NaOH ---> Na⁺ + OH⁻
NaOH is a strong base therefore it completely ionizes and releases OH⁻ ions into the medium
HCl ---> H⁺ + Cl⁻
HCl is a strong base and completely ionizes and releases H⁺ ions in to the medium. number of NaOH moles in 1 L - 0.1 mol
Therefore in x L - 0.1 /1 * x = 0.1x moles of NaOH present 
Similarly in HCl x L contains - 0.1x moles of HCl
H⁺ + OH⁻ ---> H₂O
Due to complete ionisation, 0.1x moles of H⁺ ions and 0.1x moles of OH⁻ ions react to form 0.1x moles of H₂O. Therefore all H⁺ and OH⁻are completely used up and yield water molecules.
Then at this point the H⁺ and OH⁻ ions in the medium come from the weak dissociation of water. This is equivalent to 1 x 10⁻⁷M
pH = -log [H⁺]
pH = -log [10⁻⁷]
pH = 7
pH is therefore equals to 7 which means the solution is neutral

Ithinks its false. tell me if im wrong