not to give quarter
not to give quarter {v. phr.}
1. To be utterly unwilling to show mercy; not to allow a weaker or defeated party the chance to save themselves through escape.
The occupying foreign army gave no quarter — they took no prisoners, shot everyone, and made escape impossible.
2. To argue so forcefully during a negotiation or in a court of law as to make any counter-argument or counter-proposal impossible.
The District Attorney hammered away at the witnesses and gave no quarter to the attorney for the defense.
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Source: A Dictionary of American Idioms
