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ELIMINATION

Definition:

[noun] the act of removing or getting rid of something
Synonyms: riddance
[noun] the bodily process of discharging waste matter
Synonyms: evacuation, excretion, excreting, voiding
[noun] analysis of a problem into alternative possibilities followed by the systematic elimination of unacceptable alternatives
Synonyms: reasoning by
[noun] the act of removing an unknown mathematical quantity by combining equations
[noun] the murder of a competitor
Synonyms: liquidation