Do basic solutions also have $\mathrm{H}^{+}(\mathrm{aq})$ ions ?

Question.
Do basic solutions also have $\mathrm{H}^{+}(\mathrm{aq})$ ions ? If yes, then why are these basic ?

solution:
Yes, a basic solution also has $\mathrm{H}^{+}(\mathrm{aq})$ ions. However, their concentration is less as compared to the concentration of $\mathrm{OH}^{-}(\mathrm{aq})$ ions which makes the solution basic.

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