As defined by Arrhenius: An Arrhenius acid is a substance that dissociates in water to form hydrogen ions (H+). An Arrhenius base is a substance that dissociates in water to form hydroxide (OH–) ions.
But all acids do not necessarily dissociates in water to form hydrogen ions (H+). for example Boric acid; As H3B03 is basically B(OH)3 and therefore it cannot give H+ ions.
Like this all base do not necessarily dissociates in water to form hydrogen ions (H+).for example Ammonia.ammonia does NOT contain hydroxide ions, i.e. its chemical formula is NH3, it does not fall under the Arrhenius' umbrella.