sense of false hope vs false sense of hope :

sense of false hope or false sense of hope

If you’re trying to lull someone into hopefulness you don’t want to give them a sense of false hope. Rather, you want to make them feel really hopeful, although such hope is unjustified. So what you should say is “a false sense of hope.” The same goes for similar expressions such as “false sense of security,” “false sense of confidence,” and “false sense of privacy.”

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