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Lewis bases donate electrons in a reaction with a lewis acid. In this case, F- and H- all have full set of electrons, which can form bonds with positive cations. In this sense, they are "donating" an electron pair. BF3 is missing an electron pair for a full octet, so it will form a coordinate bond with an atom that can donate it. It accepts an electron pair, making it a Lewis acid.
For ions, the basic rule is that a cation will always be an acid and a cation will be a base. To determine if molecules are a base or an acid, you can form an equation where it reacts with water and if it forms hydroxide then the molecule is a base but if it form hydronium then it is an acid.
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