prove the following: there exist integers x 390. This is an intro to prrof writing so please, if you help, show the logic form with quantifiers of the initial statement and the form for the proof you will use. TY Simply picking values will not work. The proof I am trying to use to show this would be proff by contradiction using quantifiers.

Question

prove the following: there exist integers x < 100 and y < 30 such that x + y < 128 and for all real numbers r and s, if r > x and s > y, then (r-50)(s-20) > 390. This is an intro to prrof writing so please, if you help, show the logic form with quantifiers of the initial statement and the form for the proof you will use. TY Simply picking values will not work. The proof I am trying to use to show this would be proff by contradiction using quantifiers.