Diatonic key signatures result from the diatonic scales. There are 15 diatonic scales and each of them have a key signature which corresponds to each scale. There is a circle of fifths which shows the system on how to come across each and every diatonic key signature and scale.
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a scale that is diatonic and pentatonic
The two kinds of key signatures are major and minor.
Minor and major are two diatonic scales. A minor has no key signature. The key signature of A Major is three sharps, F# C# G#.
F major, B-flat major.
In the order of flats in key signatures, even if the melody skips the B-flat, the key would contain it, because there is no such key with only an E-flat.