**Test Yourself**

Page 73

1. An _and_ statement is true when, and only when, both components are _______.

**Solution**

True.

2. An _or_ statement is false when, and only when, both components are _______.

**Solution**

False.

3. Two statement forms are logically equivalent when, and only when, they always
   have _______.

**Solution**

The same truth values.

4. De Morgan's laws says (1) that the negation of an _and_ statement is
   logically equivalent to the _______ statement in which each component is
   _______, and (2) that the negation of an _or_ statement is logically
   equivalent to the _______ statement in which each component is _______.

**Solution**

or; negated; and; negated.

5. A tautology is a statement that is always _______.

**Solution**

true

6. A contradiction is a statement that is always _______.

**Solution**

false

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**Test Yourself**

Page 86

1. An _if-then_ statement is false if, and only if, the hypothesis is _______
   and the conclusion is _______.

**Solution**

true; false

2. The negation of "if $p$ then $q$" is _______.

**Solution**

$p$ and not $q$.

$$ p \wedge \neg q $$

3. The converse of "if $p$ then $q$" is _______.

**Solution**

if $q$ then $p$

$$ q \to p $$

4. The contrapositive of "if $p$ then $q$" is _______.

**Solution**

if not $q$ then not $p$.

$$ \neg q \to \neg p $$

5. The inverse of "if $p$ then $q$" is _______.

**Solution**

if not $p$ then not $q$.

$$ \neg p \to \neg q $$

6. A conditional statement and its contrapositive are _______.

**Solution**

logically equivalent.

7. A conditional statement and its converse are not _______.

**Solution**

logically equivalent.

8. "$R$ is a sufficient condition for $S$" means "if _______ then _______."

**Solution**

$R$; $S$.

9. "$R$ is a necessary condition for $S$" means "if _______ then _______."

**Solution**

$S$; $R$

10. "$R$ only if $S$" means "if _______ then _______."

**Solution**

$R$; $S$