Chapter Review
Statements and Quantifiers
Fill in the blanks to complete the following sentences.
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
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Truth Tables for the Conditional and Biconditional
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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.