### Chapter Review

##### Statements and Quantifiers

Fill in the blanks to complete the following sentences.

*The Wall*is not a rock opera.

##### Compound Statements

Fill in the blanks to complete the following sentences.

Given: p{:} “Tweety Bird is a bird,” q{:} “Bugs is a bunny,” r{:} “Bugs says, ‘What’s up, Doc?’,” s{:} “Sylvester is a cat,” and t{:} “Sylvester chases Tweety Bird.”

Given: p{:} “Tweety Bird is a bird,” q{:} “Bugs is a bunny,” r{:} “Bugs says, ‘What’s up, Doc?’,” s{:} “Sylvester is a cat,” and t{:} “Sylvester chases Tweety Bird.”

For each of the following compound logical statements, apply the proper dominance of connectives by adding parentheses to indicate the order to evaluate the statement.

##### Constructing Truth Tables

Fill in the blanks to complete the sentences.

##### Truth Tables for the Conditional and Biconditional

Fill in the blanks to complete the following sentences.

Complete the truth tables below to determine the truth value of the proposition in the last column.

p | q | r | {p} \vee {q} | \text{~}\left( {{p} \vee {q}} \right) | \text{~}{r} | \text{~}({p} \vee {q}) \to {\text{ }}\text{~}{r} |
---|---|---|---|---|---|---|

F | F | T |

p | q | \text{~}{q} | {p} \to {q} | \text{~}\left( {{p} \to {q}} \right) | {p} \wedge \text{~}{q} | \text{~}({p} \to {q}) \leftrightarrow \left( {{p} \wedge \text{~}{q}} \right) |
---|---|---|---|---|---|---|

T | F |

\text{~}p \vee q{\text{ }} \leftrightarrow {\text{ }}\text{~}q \to {\text{ }}\text{~}p

##### Equivalent Statements

##### De Morgan’s Laws

##### Logical Arguments

Fill in the blanks to complete the sentences below.

If all frogs are brown, then Kermit is not a frog. Kermit is a frog. Therefore, some frogs are not brown.