Question 1

Convert the compound statement into words.
-$$\begin{array} { l } 
\mathrm { p } = \text { "Students are happy." } \
\mathrm { q } = \text { "Teachers are happy." } \
\sim \left( \mathrm { p } _ { \vee } \sim \mathrm { q } \right)
\end{array}$$

Accepted Answer

The given statement is the negation of a disjunction, where $p$ is "Students are happy" and $\sim q$ is "Teachers are not happy." Thus, it translates to "It is not the case that students are happy or teachers are not happy."

Question 2

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim plays football and Michael plays basketball.

Accepted Answer

The statement "Jim plays football and Michael plays basketball" is a conjunction of p and q, represented symbolically as $p \wedge q$.

Question 3

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is good, then I eat too much.

Accepted Answer

The statement "If the food is good, then I eat too much" directly translates to "If r, then p," which is symbolically represented as $r \rightarrow p$.

Question 4

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim does not play football and Michael plays basketball.

Accepted Answer

The correct symbolic representation is $\sim p \wedge q$, which translates to "Jim does not play football and Michael plays basketball."

Question 5

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is not good, I wonʹt eat too much.

Accepted Answer

The statement "If the food is not good, I won't eat too much" directly translates to "If not r, then not p," which is symbolically represented as $\sim r \rightarrow \sim p$.

Question 6

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If I eat too much, then Iʹll exercise.

Accepted Answer

The statement "If I eat too much, then I'll exercise" directly translates to "p implies q," which is symbolized as $p \rightarrow q$.

Question 7

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is good and if I eat too much, then Iʹll exercise.

Accepted Answer

The statement "If the food is good and if I eat too much, then I'll exercise" directly translates to the logical expression $( r \wedge p ) \rightarrow q$, indicating that if both r and p are true, then q will also be true.

Question 8

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-Iʹll exercise if I donʹt eat too much.

Accepted Answer

The statement "I'll exercise if I don't eat too much" can be translated to "If not p, then q," which is symbolically represented as $\sim p \rightarrow q$.

Question 9

Convert the compound statement into words.
-$\mathrm { p } =$ "People buy large houses."
$q =$ "Fossil fuels pollute the air."
$q \wedge p$

Accepted Answer

The symbol $\wedge$ represents the logical "and", so the statement $q \wedge p$ translates to "Fossil fuels pollute the air and people buy large houses."

Question 10

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-It is not the case that Jim does not play football and Michael does not play basketball.

Accepted Answer

The statement negates the conjunction of the negations of both p and q, which is accurately represented by $ \sim ( \sim p \wedge \sim q ) $.

Question 11

Convert the compound statement into words.
-$\mathrm { p } =$ "Her name is Lisa."
$q =$ "She lives in Chicago."
$\sim \mathrm { p }$

Accepted Answer

The symbol $\sim$ represents negation. Therefore, $\sim \mathrm { p }$ translates to the negation of the statement "Her name is Lisa," which is "Her name is not Lisa."

Question 12

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim does not play football or Michael plays basketball.

Accepted Answer

The statement "Jim does not play football or Michael plays basketball" translates to the logical expression $\sim p \vee q$, where $\sim p$ means "Jim does not play football" and $q$ means "Michael plays basketball". The $\vee$ symbol represents "or".

Question 13

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim does not play football or Michael does not play basketball.

Accepted Answer

The statement "Jim does not play football or Michael does not play basketball" negates both individual statements and connects them with "or", which is symbolized as $\sim p \vee \sim q$.

Question 14

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-Iʹll exercise if I eat too much.

Accepted Answer

The statement "I'll exercise if I eat too much" is a conditional statement where "I eat too much" is the hypothesis and "I'll exercise" is the conclusion, correctly represented as $p \rightarrow q$.

Question 15

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

Accepted Answer

The compound statement $(q \vee p) \wedge r$ translates to "We eat a lot or the food tastes delicious" (which is the $q \vee p$ part) and "nobody has dessert" (which is the $r$ part), making option D the correct interpretation.

Question 16

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If I exercise, then I wonʹt eat too much.

Accepted Answer

The statement "If I exercise, then I won't eat too much" directly translates to "If q, then not p," which is symbolically represented as $q \rightarrow \sim p$.

Question 17

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-The food is good and if I eat too much, then Iʹll exercise.

Accepted Answer

The statement "The food is good and if I eat too much, then I'll exercise" can be broken down into two parts: "The food is good" (r) and "if I eat too much, then I'll exercise" (p → q). The conjunction of these two parts is represented by r ∧ (p → q).

Question 18

Convert the compound statement into words.
-$\mathrm { p } =$ "Babies eat bananas."
$q =$ "Babies wear plastic bibs."
$\mathrm { p } \vee \mathrm { q }$

Accepted Answer

The symbol $\vee$ represents the logical "or" operation, meaning at least one of the statements is true. Therefore, "Babies eat bananas or babies wear plastic bibs." correctly represents $\mathrm { p } \vee \mathrm { q }$.

Question 19

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is good or if I eat too much, Iʹll exercise.

Accepted Answer

The correct symbolic representation is "If the food is good or if I eat too much, then I'll exercise," which translates to $( \mathrm { r } \vee \mathrm { p } ) \rightarrow \mathrm { q }$.

Question 20

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If I exercise, then the food wonʹt be good and I wonʹt eat too much.

Accepted Answer

The correct symbolic representation is $q \rightarrow(\sim \mathrm{r} \wedge \sim \mathrm{p})$, which translates to "If I exercise, then the food won't be good and I won't eat too much."

Quiz 3: Logic

Convert the compound statement into words. - $\begin{array} { l } \mathrm { p } = \text { "Students are happy." } \\\mathrm { q } = \text { "Teachers are happy." } \\\sim \left( \mathrm { p } _ { \vee } \sim \mathrm { q } \right) \end{array}$

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim plays football and Michael plays basketball.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is good, then I eat too much.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football and Michael plays basketball.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is not good, I wonʹt eat too much.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I eat too much, then Iʹll exercise.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is good and if I eat too much, then Iʹll exercise.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -Iʹll exercise if I donʹt eat too much.

Convert the compound statement into words. - $\mathrm { p } =$ "People buy large houses." $q =$ "Fossil fuels pollute the air." $q \wedge p$

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -It is not the case that Jim does not play football and Michael does not play basketball.

Convert the compound statement into words. - $\mathrm { p } =$ "Her name is Lisa." $q =$ "She lives in Chicago." $\sim \mathrm { p }$

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football or Michael plays basketball.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football or Michael does not play basketball.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -Iʹll exercise if I eat too much.

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

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I exercise, then I wonʹt eat too much.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -The food is good and if I eat too much, then Iʹll exercise.

Convert the compound statement into words. - $\mathrm { p } =$ "Babies eat bananas." $q =$ "Babies wear plastic bibs." $\mathrm { p } \vee \mathrm { q }$

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is good or if I eat too much, Iʹll exercise.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I exercise, then the food wonʹt be good and I wonʹt eat too much.