For each of the following statements 1 write the statement i

For each of the following statements, (1) write the statement informally without using variables or the symbols ForAll or There Exists, and (2) indicate whether the statement is true or false and briefly justify your answer. ForAll real numbers x, There Exists a real number y such that x

Solution

(a) For every real number x, there exists a real number y such that x < y

The statement is TRUE, since for every real number there exists a real number y such that x < y

(b) There exists a real number y such that for all real numbers x, x < y

The statement is FALSE, since we cant\'t defined a maximum value for a number y which is greater than all x, hence the statement is not TRUE