Under what condition did georgia say it would stay it the union (united states) for?

the fourth amendment protects:

"the right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."  

so this would mean the denial to search and seizure without warrant or permission.

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