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There are three definitions for acids and bases.

Arrhenius definition: An acid is a substance that produces hydrogen (H+) ions in water while a base produces hydroxide (OH-) ions.

Bronsted-Lowry definition: An acid gives up or donates a proton (H+) to another molecule while a base accepts a proton.

Lewis definition: An acid accepts an electron pair in bonding to another molecule/ion while a base donates and electron pair.

Note that if a substance meets one of the first two definitions it probably meets the others as well.

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