118 lines
1.9 KiB
Markdown
118 lines
1.9 KiB
Markdown
**Test Yourself**
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Page 73
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1. An _and_ statement is true when, and only when, both components are _______.
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**Solution**
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True.
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2. An _or_ statement is false when, and only when, both components are _______.
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**Solution**
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False.
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3. Two statement forms are logically equivalent when, and only when, they always
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have _______.
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**Solution**
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The same truth values.
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4. De Morgan's laws says (1) that the negation of an _and_ statement is
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logically equivalent to the _______ statement in which each component is
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_______, and (2) that the negation of an _or_ statement is logically
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equivalent to the _______ statement in which each component is _______.
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**Solution**
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or; negated; and; negated.
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5. A tautology is a statement that is always _______.
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**Solution**
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true
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6. A contradiction is a statement that is always _______.
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**Solution**
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false
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---
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**Test Yourself**
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Page 86
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1. An _if-then_ statement is false if, and only if, the hypothesis is _______
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and the conclusion is _______.
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**Solution**
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true; false
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2. The negation of "if $p$ then $q$" is _______.
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**Solution**
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$p$ and not $q$.
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$$ p \wedge \neg q $$
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3. The converse of "if $p$ then $q$" is _______.
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**Solution**
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if $q$ then $p$
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$$ q \to p $$
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4. The contrapositive of "if $p$ then $q$" is _______.
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**Solution**
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if not $q$ then not $p$.
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$$ \neg q \to \neg p $$
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5. The inverse of "if $p$ then $q$" is _______.
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**Solution**
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if not $p$ then not $q$.
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$$ \neg p \to \neg q $$
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6. A conditional statement and its contrapositive are _______.
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**Solution**
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logically equivalent.
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7. A conditional statement and its converse are not _______.
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**Solution**
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logically equivalent.
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8. "$R$ is a sufficient condition for $S$" means "if _______ then _______."
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**Solution**
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$R$; $S$.
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9. "$R$ is a necessary condition for $S$" means "if _______ then _______."
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**Solution**
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$S$; $R$
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10. "$R$ only if $S$" means "if _______ then _______."
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**Solution**
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$R$; $S$
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