**Test Yourself**

Page 141

1. If $P(x)$ is a predicate with domain $D$, the truth set of $P(x)$ is denoted
   _______. We read these symbols out loud as _______.

$\{x \in D | P(x)\}$; "the set of all $x$ in $D$ such that $P(x)$."

2. Some ways to express the symbol $\forall$ in words are _______.

for every for all, for any, for each, for arbitrary, given any

3. Some ways to express the symbol $\exists$ in words are _______.

there exists, there exist, there exists at least one, for some, for at least
one, we can find a

4. A statement of the form $\forall x \in D$, $Q(x)$ is true if, and only if,
   $Q(x)$ is _______ for _______.

true; every $x$ in $D$.

5. A statement of the form $\exists x \in D$ such that $Q(x)$ is true if, and
   only if, $Q(x)$ is _______ for _______.

true; at least one $x$ in $D$.

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**Test Yourself**

Page 152

1. A negation for "All $R$ have property $S$" is "There is _______ $R$ that
   _______."

exists at least one; does not have property $S$.

2. A negation for "Some $R$ have property $S$" is "_______."

"No $R$ have property $S$."

3. A negation for "For every $x$, if $x$ has property $P$ then $x$ has property
   $Q$" is "_______."

"There exists at least one $x$ such that $x$ has property $P$ and $x$ does not
have property $Q$."

4. The converse of "For every $x$, if $x$ has property $P$ then $x$ has property
   $Q$" is "_______."

"For every $x$, if $x$ has property $Q$ then $x$ has property $P$."

5. The contrapositive of "For every $x$, if $x$ has property $P$ then $x$ has
   property $Q$" is "_______."

"For every $x$, if $x$ does not have property $Q$, then $x$ does not have
property $P$."

6. The inverse of "For every $x$, if $x$ has property $P$ then $x$ has property
   $Q$" is "_______."

"For every $x$, if $x$ does not have property $P$, then $x$ does not have
property $Q$."