examday

/TMUA

For a real number $a$, consider the equation

Define

$P:$ For every real $x$, there exists a real $y$ satisfying the equation,

$Q:$ For every real $y$, there exists a real $x$ satisfying the equation,

$R:$ $a>0$.

Which statements are true?

• I. $P$ if and only if both $Q$ and $R$ are true.
• II. $Q$ only if at least one of $P$ and not $R$ is true.
• III. $R$ only if at least one of $P$ and not $Q$ is true.