ausschließen
to exclude
To keep or remove someone or something from a group, place, or activity.
Wegen seines Verhaltens wurde er vom Verein ausgeschlossen.
Because of his behavior, he was excluded from the club.

to exclude / rule out
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to exclude
To keep or remove someone or something from a group, place, or activity.
Wegen seines Verhaltens wurde er vom Verein ausgeschlossen.
Because of his behavior, he was excluded from the club.

'Ausschließen' is a separable verb. The prefix 'aus' goes at the end in a main clause. In a subordinate clause, the verb stays together.
Der Schiedsrichter schloss den Spieler nach dem Foul aus.
The referee excluded the player after the foul.
The verb is made up of 'aus' (out) and 'schließen' (to close, to lock). The literal meaning is therefore to leave someone or something outside by closing the door.
Er hat den Hund aus dem Schlafzimmer ausgeschlossen.
He kept the dog out of the bedroom.
When you exclude someone from an activity or group, the preposition 'von' is used with the dative. The structure is: 'jemanden von etwas ausschließen' (to exclude someone from something).
Sie wurde von der weiteren Teilnahme am Wettbewerb ausgeschlossen.
She was excluded from further participation in the competition.
To describe a possibility as unlikely, the construction 'nicht ausschließen können, dass ...' (not be able to rule out that ...) is often used. It is followed by a subordinate clause.
Ich kann nicht ausschließen, dass ich einen Fehler gemacht habe.
I can't rule out that I made a mistake.
The reflexive form 'sich ausschließen' has a very specific, everyday meaning: you have closed the door behind you and forgotten the key.
Sei vorsichtig mit der Tür, damit du dich nicht ausschließt.
Be careful with the door so you don't lock yourself out.
to record / take in
'aufnehmen' and 'ausschließen' are opposites when it comes to groups, places, or activities. 'aufnehmen' means that someone becomes part of a group or is accommodated somewhere. 'ausschließen' means that someone is not allowed to participate or is removed from a group. Use 'aufnehmen' when someone joins or is taken in, and 'ausschließen' when someone has to stay out.

Der Verein schließt niemanden wegen seiner Herkunft aus.
The club does not exclude anyone because of their background.
Wir nehmen den neuen Nachbarn in unsere Laufgruppe auf.
We are taking the new neighbor into our running group.