mutually exclusive

Two events (see sample space), A and B, are exclusive if they cannot both occur simultaneously, i.e. if A ∩ B=ϕ, the empty set. In this case P(A ∩ B)=0. The n events A₁, A₂,..., A_n are mutually exclusive if, for all j≠k, A_j ∩ A_k=ϕ.

Describing an instance where the occurrence of one event precludes the occurrence of a second event; for example, if a long-distance runner dies during a track meet, the runner cannot enter future track meets.

The adjective has 2 meanings:

Meaning #1: unable to be both true at the same time
  Synonym: contradictory

Meaning #2: necessitating a choice between mutually exclusive possibilities
  Synonym: alternative