should there be any death sentence? do we have right to kill ?

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"kill the sin and not the sinner".if this is true then why do we legally give death sentence to the people.the recent case is the death sentence given to danunjay chatergee,who has been convicted of raping a minor girl and murdering her.but the death sentence was given to him after 8 years.this happened in india, one of the greatest democracy.danunjay was the only earner in his very poor family.the social circumstances around him were also responsible.