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Q: Why did David say the rich man should die?

A: David said the rich man in Nathan's parable should die because He was outraged by the man's injustice in stealing and killing a poor man's only lamb to feed a visitor. 

Q: What did Nathan say would happen to David because of the what he did to Uriah?

A:A: Nathan told David that because of his adultery with Bathsheba and the murder of Uriah the sword would never depart from his house own household would rebel against him and his wives would be taken and slept with in public view.