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Denials and Negations

Please solve for #7 and the problems marked by * in #10.
Actually there is no prerequisites for the problems. For #7, you just need to decide the statement can be a mathematical proposition or not.

College level proof before real analysis. Please give formal proof.
Please explain each step of your solution. Thank you.


Solution Summary

Denials and negations are provided. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.