Determine the truth vale of each of these statements if the

Determine the truth vale of each of these statements if the domain of each variable consists of all integers. x y(x + 4 = y) x y(x - y = y - x) x y(x + y = 10) x y(((x > 0) (y

Solution

a) For every X, there exists a y such that (x+4) = y

The given statement isTRUE, since for evert integer x there exists an integer y = x + 4

b) There exists an x an y such that (x-y) = (y-x)

(x-y) = (y-x)

x = y, hence the statement is FALSE, since the value of x=y must be there for this statement

c) There exists an x for every y such that (x+y) = 10

The statement is TRUE

d) The statement is TRUE, since xor of one negative number and one positive number is always negatve