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Yes, the conjugate see-saw applies both ways. This means that if an acid is very strong then its conjugate base will be very weak. Additionally, if a base is very strong then its conjugate acid will be very weak. This can be shown through the equation Ka x Kb =Kw. If an acid has a very high Ka then its Kb will be very low as the two are inverse in comparison to the Kw constant 1x10^-14.
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