Two statements are mutual excusives (and hence, mutually excusive) if they are each given as excuses as to why one can't take part in the other, whilst hiding one's genuine plans.
Sarah: "Sorry Dave, I can't come to the cinema with you later, because I told Louise that we'd have a girls' night in."
Sarah: "Sorry Louise, I can't come to girls' night, I promised Dave that I'd go to the cinema with him."
Thus, "going to the cinema with Dave" and "having a girl's night in with Louise" are mutually excusive.
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