a) Form the negation of the following statements about a set S CR of real numbers....

 

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a) Form the negation of the following statements about a set S CR of real numbers. (1) Ve > 03N E S Vn e N: (n > N =< e). (ii) Væ e [0, 1] Ve >03N E S Vn e N: (n > N = x" < e). b) Decide whether the statements in (a) are true or false when S = N. Justify your answer. c) Consider the following plain English' statements. Every apartment has a room with beds. Every apartment with at least two rooms also has a balcony. Express these statements using logic symbols such as "V, 3, and, or", etc. Form the negation of the formal statements, and re-express in plain English. a) Form the negation of the following statements about a set S CR of real numbers. (1) Ve > 03N E S Vn e N: (n > N =< e). (ii) Væ e [0, 1] Ve >03N E S Vn e N: (n > N = x" < e). b) Decide whether the statements in (a) are true or false when S = N. Justify your answer. c) Consider the following plain English' statements. Every apartment has a room with beds. Every apartment with at least two rooms also has a balcony. Express these statements using logic symbols such as "V, 3, and, or", etc. Form the negation of the formal statements, and re-express in plain English.