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the acid or base will dissociate completely. For acids, it will give away all of its H+ ions and bases will give off it's OH- completely. After being dissolved in water, there will be nothing left of that acid or base in terms of concentration.
It means they dissociate completely in solution. This correlates to being strong because it means that there are more H+ or OH- ions in the solution, making it more acidic or basic respectively.
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