Note
we don't use 'with' (mit) here in German. It would mean that they both sit down together. Since the woman sits already, the man is sitting down 'to' the woman: zu.Breakdown of Er setzt sich zu der Frau.
die Frau
the woman
er
he
sich setzen
to sit down
important: this is a movement towards a direction (down) you are standing and moving into a sitting position.
zu
to; at
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