Question 1

Write the compound statement in words.
-Let $\mathbf { r } =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$q =$ "His owners are happy."
$r \wedge ( p - q )$

Accepted Answer

The statement $r \wedge ( p \rightarrow q )$ translates to "The puppy is trained, and if the puppy behaves well then his owners are happy," which matches option C.

Question 2

Construct a truth table for the statement.
-$r \vee \sim(c \wedge q)$

Accepted Answer

The correct truth table for $r \vee \sim(c \wedge q)$ reflects that the statement is true unless $r$ is false and both $c$ and $q$ are true, which is accurately represented in option B.

Question 3

Convert the compound statement into words.
-$$\begin{array} { l } 
\mathrm { p } = \text { "The food tastes delicious." } \
\mathrm { q } = \text { "We eat a lot." } \
\mathrm { r } = \text { "Nobody has dessert." } \
\sim \mathrm { q } \vee ( \mathrm { p } \wedge \mathrm { r } )
\end{array}$$

Accepted Answer

The logical statement $\sim q \vee (p \wedge r)$ translates to "We do not eat a lot or the food tastes delicious and nobody has dessert." This is because $\sim q$ means "not q" (We do not eat a lot), $\vee$ means "or", $p \wedge r$ means "p and r" (the food tastes delicious and nobody has dessert).

Question 4

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-If tomorrow is not Saturday then today is Friday if and only if tomorrow is Saturday.

Accepted Answer

The answer of Select letters to represent the simple statements...

Question 5

Construct a truth table for the statement.
-$(P \wedge \sim t) \wedge s$

Accepted Answer

The correct truth table for $(P \wedge \sim t) \wedge s$ reflects that the statement is true only when $P$ is true, $t$ is false (since $\sim t$ inverts the truth value of $t$), and $s$ is true. This is accurately represented in option B, where the only true outcome occurs under these conditions.

Question 6

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-It is not true that if you take your vitamins you will stay healthy.

Accepted Answer

The statement is a negation of a conditional statement, where $p$ represents "you take your vitamins" and $q$ represents "you will stay healthy". The correct symbolic representation is $\sim ( p \rightarrow q )$, indicating it is not true that if $p$ then $q$.

Question 7

Write the compound statement in words.
-Let $\mathrm { r } =$ "The puppy is trained."
$\begin{array} { l } 
\quad \mathrm { p } = \text { "The puppy behaves well." } \
\mathrm { q } = \text { "His owners are happy." } \
\sim ( p \rightarrow q )
\end{array}$

Accepted Answer

The symbol $\sim ( p \rightarrow q )$ translates to "It is not the case that if the puppy behaves well then his owners are happy," which negates the conditional statement "if the puppy behaves well then his owners are happy."

Question 8

Answer the question.
-A restaurant has the following statement on the menu: ʺAll dinners are served with a choice of: Soup or Salad, and Potatoes or Pasta, and Corn or Beans.ʺ A customer asks for salad, potatoes, And pasta. Is this order permissible?

Accepted Answer

The statement specifies a choice between options (Soup or Salad, and Potatoes or Pasta), not both/all, so the customer's request for both potatoes and pasta is not permissible according to the menu's options.

Question 9

Construct a truth table for the statement.
-$\sim \mathrm { r } \wedge \sim \mathrm { q }$

Accepted Answer

The correct truth table for $\sim r \wedge \sim q$ shows that the statement is true only when both $r$ and $q$ are false, as indicated by the combination of negations ($\sim$) and the conjunction ($\wedge$).

Question 10

Write the compound statement in words.
-Let $\mathbf { r } =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$q =$ "His owners are happy."
$( \sim \mathbf { r } v \sim \mathrm { p } ) \rightarrow \sim \mathrm { q }$

Accepted Answer

The compound statement $( \sim \mathbf { r } v \sim \mathrm { p } ) \rightarrow \sim \mathrm { q }$ translates to "If the puppy is not trained or the puppy does not behave well, then his owners are not happy," which matches option B.

Question 11

Write the compound statement in words.
-Let $r =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$\mathrm { q } =$ "His owners are happy."
$\mathrm { p } \rightarrow \mathrm { r }$

Accepted Answer

The statement $\mathrm { p } \rightarrow \mathrm { r }$ translates to "If $\mathrm { p }$ then $\mathrm { r }$," which in words is "If the puppy behaves well then the puppy is trained."

Question 12

Write the compound statement in words.
-Let $\mathrm { p } =$ "The monitor is included."
$\mathrm { q } =$ "The color printer is optional."
$r =$ "The zip drive is extra."
$\sim ( p \wedge q ) \rightarrow ( r \vee \sim q )$

Accepted Answer

The answer of Write the compound statement in words.
-Let \(\mathrm...

Question 13

Write the compound statement in words.
-Let $r =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
 $\mathrm { q } =$ "His owners are happy."
$\sim \mathrm { r } \rightarrow \sim \mathrm { q }$

Accepted Answer

The statement $\sim r \rightarrow \sim q$ translates to "If the puppy is not trained, then his owners are not happy," which matches option A.

Question 14

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-If people drive small cars then people will use less fuel and the ozone hole will not expand.

Accepted Answer

The correct symbolic representation is $ p \rightarrow ( q \wedge \sim r ) $, which is a conditional statement. It correctly translates to "If people drive small cars (p) then people will use less fuel (q) and the ozone hole will not expand (\sim r)."

Question 15

Write the compound statement in words.
-Let $\mathrm { p } =$ "The monitor is included."
$\mathrm { q } =$ "The color printer is optional."
$\mathrm { r } =$ "The zip drive is extra."
$\mathrm { q } \leftrightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$

Accepted Answer

The statement $\mathrm { q } \leftrightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$ translates to "The color printer is optional if and only if the monitor is not included and the zip drive is extra," which matches choice D.

Question 16

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-If a number is divisible by 3 and the number is not divisible by 2 then the number is not divisible By 6.

Accepted Answer

The statement is a conditional statement because it has the form "if...then...". It states that if a number is divisible by 3 and not divisible by 2, then it is not divisible by 6. This is represented by $( \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow ( \sim \mathrm { r } )$, where $p$ is "a number is divisible by 3", $\sim q$ is "the number is not divisible by 2", and $\sim r$ is "the number is not divisible by 6".

Question 17

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-Pat Rabbit did not go into Mr. McNoodleʹs garden and Molly collected blueberries.

Accepted Answer

The statement is a conjunction because it combines two simple statements: "Pat Rabbit did not go into Mr. McNoodle's garden" and "Molly collected blueberries" using "and". The symbol $\sim p$ represents the negation of Pat Rabbit going into the garden, and $q$ represents Molly collecting blueberries. The $\wedge$ symbol is used for "and", making the statement a conjunction.

Question 18

Write the compound statement in words.
-Let $\mathrm { r } =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$q =$ "His owners are happy."
$r \rightarrow ( p \wedge q )$

Accepted Answer

The statement $r \rightarrow ( p \wedge q )$ translates to "If the puppy is trained, then the puppy behaves well and his owners are happy," which matches choice A.

Question 19

Write the compound statement in words.
-Let $r =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$\mathrm { q } =$ "His owners are happy."
$( r \wedge p ) \rightarrow  q$

Accepted Answer

The compound statement $( r \wedge p ) \rightarrow q$ translates to "If the puppy is trained and the puppy behaves well, then his owners are happy."

Question 20

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-The lights are on if and only if it is not midnight or it is wintertime.

Accepted Answer

The correct symbolic representation of the statement "The lights are on if and only if it is not midnight or it is wintertime" is a biconditional statement, which is correctly represented in option A as $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$. This means "p if and only if not q or r".

Quiz 3: Logic

Write the compound statement in words. -Let $\mathbf { r } =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." $r \wedge ( p - q )$

Construct a truth table for the statement. - $r \vee \sim(c \wedge q)$

Convert the compound statement into words. - $\begin{array} { l } \mathrm { p } = \text { "The food tastes delicious." } \\\mathrm { q } = \text { "We eat a lot." } \\\mathrm { r } = \text { "Nobody has dessert." } \\\sim \mathrm { q } \vee ( \mathrm { p } \wedge \mathrm { r } ) \end{array}$

Construct a truth table for the statement. - $(P \wedge \sim t) \wedge s$

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -It is not true that if you take your vitamins you will stay healthy.

Write the compound statement in words. -Let $\mathrm { r } =$ "The puppy is trained." $\begin{array} { l } \quad \mathrm { p } = \text { "The puppy behaves well." } \\\mathrm { q } = \text { "His owners are happy." } \\\sim ( p \rightarrow q ) \end{array}$

Answer the question. -A restaurant has the following statement on the menu: ʺAll dinners are served with a choice of: Soup or Salad, and Potatoes or Pasta, and Corn or Beans.ʺ A customer asks for salad, potatoes, And pasta. Is this order permissible?

Construct a truth table for the statement. - $\sim \mathrm { r } \wedge \sim \mathrm { q }$

Write the compound statement in words. -Let $\mathbf { r } =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." $( \sim \mathbf { r } v \sim \mathrm { p } ) \rightarrow \sim \mathrm { q }$

Write the compound statement in words. -Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $\mathrm { q } =$ "His owners are happy." $\mathrm { p } \rightarrow \mathrm { r }$

Write the compound statement in words. -Let $\mathrm { p } =$ "The monitor is included." $\mathrm { q } =$ "The color printer is optional." $r =$ "The zip drive is extra." $\sim ( p \wedge q ) \rightarrow ( r \vee \sim q )$

Write the compound statement in words. -Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $\mathrm { q } =$ "His owners are happy." $\sim \mathrm { r } \rightarrow \sim \mathrm { q }$

Write the compound statement in words. -Let $\mathrm { p } =$ "The monitor is included." $\mathrm { q } =$ "The color printer is optional." $\mathrm { r } =$ "The zip drive is extra." $\mathrm { q } \leftrightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -Pat Rabbit did not go into Mr. McNoodleʹs garden and Molly collected blueberries.

Write the compound statement in words. -Let $\mathrm { r } =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." $r \rightarrow ( p \wedge q )$

Write the compound statement in words. -Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $\mathrm { q } =$ "His owners are happy." $( r \wedge p ) \rightarrow q$

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -The lights are on if and only if it is not midnight or it is wintertime.

Quiz 3: Logic

Write the compound statement in words. -Let r=\mathbf { r } =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=q =q= "His owners are happy." r∧(p−q) r \wedge ( p - q ) r∧(p−q)

Construct a truth table for the statement. - r∨∼(c∧q) r \vee \sim(c \wedge q) r∨∼(c∧q)

Construct a truth table for the statement. - (P∧∼t) ∧s(P \wedge \sim t) \wedge s(P∧∼t) ∧s

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. -It is not true that if you take your vitamins you will stay healthy.

Answer the question. -A restaurant has the following statement on the menu: ʺAll dinners are served with a choice of: Soup or Salad, and Potatoes or Pasta, and Corn or Beans.ʺ A customer asks for salad, potatoes, And pasta. Is this order permissible?

Construct a truth table for the statement. - ∼r∧∼q\sim \mathrm { r } \wedge \sim \mathrm { q }∼r∧∼q

Write the compound statement in words. -Let r=\mathbf { r } =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=q =q= "His owners are happy." (∼rv∼p) →∼q( \sim \mathbf { r } v \sim \mathrm { p } ) \rightarrow \sim \mathrm { q }(∼rv∼p) →∼q

Write the compound statement in words. -Let r=r =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=\mathrm { q } =q= "His owners are happy." p→r\mathrm { p } \rightarrow \mathrm { r }p→r

Write the compound statement in words. -Let p=\mathrm { p } =p= "The monitor is included." q=\mathrm { q } =q= "The color printer is optional." r=r =r= "The zip drive is extra." ∼(p∧q) →(r∨∼q) \sim ( p \wedge q ) \rightarrow ( r \vee \sim q ) ∼(p∧q) →(r∨∼q)

Write the compound statement in words. -Let r=r =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=\mathrm { q } =q= "His owners are happy." ∼r→∼q\sim \mathrm { r } \rightarrow \sim \mathrm { q }∼r→∼q

Write the compound statement in words. -Let p=\mathrm { p } =p= "The monitor is included." q=\mathrm { q } =q= "The color printer is optional." r=\mathrm { r } =r= "The zip drive is extra." q↔(∼p∧r) \mathrm { q } \leftrightarrow ( \sim \mathrm { p } \wedge \mathrm { r } ) q↔(∼p∧r)

Write the compound statement in words. -Let r=\mathrm { r } =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=q =q= "His owners are happy." r→(p∧q) r \rightarrow ( p \wedge q ) r→(p∧q)

Write the compound statement in words. -Let r=r =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=\mathrm { q } =q= "His owners are happy." (r∧p) →q( r \wedge p ) \rightarrow q(r∧p) →q