Let $P(x)$ be the predicate $"x>\frac{1}{x}".$

$($a$)$ Write $P(2),P(\frac{1}{2}),P(-1),P(-\frac{1}{2}),$ and $P(-8),$ and indicate which

of these statements are true and which are false.

$($b$)$ Find the truth set of $P(x)$ if the domain of $x$ is $R,$ the set of all real

numbers.

$($c$)$ If the domain is the set $R^{+}$of all positive real numbers, what is the

truth set of $P(x)?$Let P $($x$)$ be the predicate $$x $>1$

x $.$

$($a$)$ Write P $(2),$ P $1$

$2$

$,$ P $(1),$ P $1$

$2$

$,$ and P $(8),$ and indicate which

of these statements are true and which are false.

$($b$)$ Find the truth set of P $($x$)$ if the domain of x is R$,$ the set of all real

numbers.

$($c$)$ If the domain is the set R$+$ of all positive real numbers, what is the

truth set of P $($x$)?$