P(x, y) means "x and y are real numbers such that $$x + 2 y = 5 "$$
Determine whether the statement
is true.
-$$\exists x \forall y P ( x , y )$$ In 73-75 P(m, n) means $$“ m \leq n "$$
where the universe of discourse for m and n is the set of nonnegative
integers. What is the truth value of the statement?

Question

P(x, y) means "x and y are real numbers such that $$x + 2 y = 5 "$$
 Determine whether the statement
is true.
-$$\exists x \forall y P ( x , y )$$ In 73-75 P(m, n) means $$“ m \leq n "$$
 where the universe of discourse for m and n is the set of nonnegative
integers. What is the truth value of the statement?

Quizplus · Accepted Answer

The statement $\exists x \forall y P(x, y)$ implies there exists a real number $x$ such that for all real numbers $y$, $x + 2y = 5$. However, for any fixed $x$, $x + 2y = 5$ cannot hold for all $y$ since $y$ can take any real value, making the equation impossible to satisfy universally.

P(x, Y) Means "X and Y Are Real Numbers Such x+2y=5"x + 2 y = 5 "x+2y=5"

P(x, Y) Means "X and Y Are Real Numbers Such $x + 2 y = 5 "$