I checked online for the manual for the PSR-F51, and I must admit, unless I'm missing something, the information about automatic chords seems pretty thin in this manual. There is the following statement in the section on styles...
"The Styles add excitement to your performance—
giving you authentic, automatic backing in a wide
variety of music genres. Just play chords (or even single-
note chords) with your left hand, and enjoy the
accompaniment of a full band behind you!"
So, it does mention the possibility of "single-note chords", but does not give details about how they work. If I had to guess, it probably works like the single-finger chords on the E-series keyboards, but I have no direct experience with this keyboard. If it does work like the E-series, then playing a single note in the left-hand chord part of the keyboard gives you a major chord, playing a note and the closest black key below that note gives you the minor chord of the top note you're playing, playing a note and the closest white key below that note gives you the 7th chord of the top note you're playing, and playing a note and the closest black and white keys (together) below that note gives you the minor-7th chord of the top note you're playing.
And, again if it is like the E-series, the keyboard would automatically recognize if you're playing an actual chord, and act accordingly. In other words, if you're playing one of the single-notes or 2 or 3 note clusters I described above, you get the "easy-play" chords. But if you play an actual chord, such as C, Eb, and G for C minor, or D, F#, and A for D major, then the keyboard will recognize that chord and give you a style accompaniment with that chord when you have a style playing, and it should recognize the different inversions of these chords, as well. Again, this is all speculation. I would recommend trying this out yourself to be sure before buying the keyboard.
One other thing. On the E-series keyboards, there is an accompaniment on/off button, and when you have accompaniment off, it allows you to play the whole keyboard as normal (no automatic instrumental style backing or easy-play chords), but still have the drums of the style play. It seems that this function is done with the "mute" button on the F51. Apparently, if you turn on a style, it automatically has auto-accompaniment and easy-play chords activated. But if you then hit the "mute" button, it turns off the automatic backing accompaniment and easy-play chords to allow the full length of the keyboard to be played normally, but still allows you to play along with the drums of the style. From the manual:
"Mute the instrumental backing of the Style and
play only the rhythm. While a Style is playing,
press the [MUTE] button. This also lets you play over
the full range of the keyboard while the drums/per-
cussion are playing. To restore full Style playback,
press the [MUTE] button again and play a chord in
the auto accompaniment section of the keyboard."
