Question 1

Write a negation for the statement.
-No fifth graders play soccer.
A)Not all fifth graders play soccer.
B)At least one fifth grader plays soccer.
C)All fifth graders play soccer.
D)No fifth grader does not play soccer.

Accepted Answer

The negation of "No fifth graders play soccer" is "At least one fifth grader plays soccer," because it directly contradicts the original statement by asserting that there is at least one exception.

Question 2

Convert the symbolic compound statement into words.
-p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago."
Translate the following compound statement into words: $p \wedge q$
A)Her name is Lisa and she lives in Chicago.
B)Her name is Lisa or she lives in Chicago.
C)If her name is Lisa, she lives in Chicago.
D)Her name is Lisa and she doesn't live in Chicago.

Accepted Answer

The symbol $\wedge$ represents the logical "and," so the statement $p \wedge q$ translates to "Her name is Lisa and she lives in Chicago."

Question 3

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-Jim does not play football and Michael plays basketball. 
A) $\sim p \wedge q$
B) $p \wedge q$
C) $\sim ( p \wedge q )$
D) $\sim p \vee q$

Accepted Answer

The statement "Jim does not play football and Michael plays basketball" can be symbolized as $\sim p \wedge q$, where $\sim p$ means "Jim does not play football" and $q$ means "Michael plays basketball". The conjunction $\wedge$ indicates "and".

Question 4

Write a negation for the statement.
-Some people don't like walking.
A)Some people don't like driving.
B)Nobody likes walking.
C)Some people like walking.
D)Everyone likes walking.

Accepted Answer

The negation of "Some people don't like walking" is "Everyone likes walking," which means there are no exceptions to people liking walking.

Question 5

Write a negation for the statement.
-Not all people like football.
A)Some people like football.
B)Some people do not like football.
C)All people do not like football.
D)All people like football.

Accepted Answer

The negation of "Not all people like football" is "All people like football," which directly contradicts the original statement by asserting that there are no exceptions to the liking of football.

Question 6

Convert the symbolic compound statement into words.
-p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston."
Translate the following compound statement into words: $p \vee q$
A)It's raining in Chicago or it's windy in Boston.
B)It's raining in Chicago and it's windy in Boston.
C)If it's raining in Chicago, it's not windy in Boston.
D)It's not the case that it's raining in Chicago and windy in Boston.

Accepted Answer

The symbol $\vee$ represents the logical "or," so the statement translates to "It's raining in Chicago or it's windy in Boston."

Question 7

Convert the symbolic compound statement into words.
-p represents the statement "It's Monday." q represents the statement "It's raining today."
Translate the following compound statement into words: $\sim \mathrm { p } \vee \sim \mathrm { q }$
A)It's Monday or it's raining today.
B)It's Monday and it's raining today.
C)It's not Monday or it's not raining today.
D)It's not Monday and it's not raining today.

Accepted Answer

The given compound statement $\sim \mathrm { p } \vee \sim \mathrm { q }$ translates to "It's not Monday or it's not raining today." This is because $\sim$ represents negation (not) and $\vee$ represents disjunction (or).

Question 8

Write a negation for the statement.
-She earns more than me.
A)She does not earn less than me.
B)She does not earn more than me.
C)She earns less than me.
D)She earns the same as me.

Accepted Answer

The correct negation of "She earns more than me" is "She does not earn more than me," which directly contradicts the original statement without implying a specific alternative (such as earning less or the same).

Question 9

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-Neither Jim plays football nor Michael plays basketball. 
A) $\sim ( p \wedge q )$
B) $\sim p \wedge q$
C) $\sim ( p \vee q )$
D) $\sim \mathrm { p } \vee \sim \mathrm { q }$

Accepted Answer

The statement "Neither Jim plays football nor Michael plays basketball" is equivalent to saying "It is not the case that Jim plays football or Michael plays basketball", which is symbolically represented as $\sim ( p \vee q )$.

Question 10

Write a negation of the inequality. Do not use a slash symbol.
-$x < 5$
A) $x < - 5$
B) $x > 5$
C) $x = 5$
D) $x \geq 5$

Accepted Answer

The negation of $x < 5$ includes $x = 5$ and $x > 5$, which is correctly represented by $x \geq 5$.

Question 11

Convert the symbolic compound statement into words.
-p represents the statement : "Students are happy." q represents the statement: "Teachers are happy."
Translate the following compound statement into words: $\sim ( p \vee \sim q )$
A)Students are not happy and teachers are not happy.
B)Students are not happy or teachers are not happy.
C)It is not the case that students are happy or teachers are not happy.
D)It is not the case that students are happy and teachers are not happy.

Accepted Answer

The given compound statement $\sim ( p \vee \sim q )$ translates to "It is not the case that students are happy or teachers are not happy." This is because $\sim$ negates the entire statement inside the parentheses, $p \vee \sim q$ means "students are happy or teachers are not happy," and the negation flips this to indicate it is not the case that this condition is met.

Question 12

Write a negation of the inequality. Do not use a slash symbol.
-$x \leq 12$
A) $x > - 12$
B) $x \leq - 12$
C) $x \geq 12$
D) $x > 12$

Accepted Answer

The negation of $x \leq 12$ is $x > 12$, as it represents all values not less than or equal to 12.

Question 13

Write a negation for the statement.
-Some athletes are musicians.
A)Some athletes are not musicians.
B)No athlete is a musician.
C)Not all athletes are musicians.
D)All athletes are musicians.

Accepted Answer

The correct negation of "Some athletes are musicians" is "No athlete is a musician," which directly contradicts the original statement by asserting that there are no athletes who are musicians.

Question 14

Write a negation of the inequality. Do not use a slash symbol.
-$x > 69$
A) $x = 69$
B) $x < 69$
C) $x \leq 69$
D) $x < - 69$

Accepted Answer

The negation of $x > 69$ includes $x$ being equal to 69 or less than 69, which is correctly represented by $x \leq 69$.

Question 15

Convert the symbolic compound statement into words.
-p represents the statement: " $x < 1$ "
q represents the statement: " $y > 1$ "
Translate the following compound statement into words: $\mathrm { p } \vee\sim \mathrm { q }$
A) $\mathrm { x }$ is less than 1 and $\mathrm { y }$ is not greater than 1 .
B) $x$ is less than 1 or $y$ is less than 1 .
C) $x$ is less than 1 or $y$ is not greater than 1 .
D) $x$ is not less than 1 and $y$ is not less than 1

Accepted Answer

The symbol $\vee$ represents "or" and $\sim$ represents "not." Therefore, $\mathrm { p } \vee\sim \mathrm { q }$ translates to "x is less than 1 or y is not greater than 1."

Question 16

Convert the symbolic compound statement into words.
-p represents the statement "It's Monday." q represents the statement "It's raining today."
Translate the following compound statement into words: $\sim p \wedge \sim q$
A)It's not Monday or it's not raining today.
B)It's not Monday and it's not raining today.
C)It's not the case that it's Monday and raining today.
D)It's Monday or it's raining today.

Accepted Answer

The symbol $\sim$ represents negation, and $\wedge$ represents conjunction (and). Therefore, $\sim p \wedge \sim q$ translates to "It's not Monday and it's not raining today."

Question 17

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-Jim does not play football and Michael does not play basketball. 
A) $\sim ( p \wedge q )$
B) $\sim p \wedge q$
C) $\sim \mathrm { p } \mathrm {} \vee \sim \mathrm { q }$
D) $\sim \mathrm { p } \wedge \sim \mathrm { q }$

Accepted Answer

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

Question 18

Write a negation of the inequality. Do not use a slash symbol.
-$x \geq - 50$
A) $x \geq 50$
B) $x < 50$
C) $x < - 50$
D) $x \leq - 50$

Accepted Answer

The negation of $x \geq -50$ is $x < -50$, which changes the direction of the inequality and does not change the number.

Question 19

Convert the symbolic compound statement into words.
-p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: $\sim p$
A) She does not live in Chicago.
B) It is true her name is Lisa.
C) Her name is Teresa.
D) Her name is not Lisa.

Accepted Answer

The symbol $\sim p$ translates to "not p," which means the opposite of the statement represented by $p$. Since $p$ is "Her name is Lisa," $\sim p$ means "Her name is not Lisa."

Question 20

Write a negation for the statement.
-Everyone is asleep.
A)Not everyone is asleep.
B)Nobody is awake.
C)Everyone is awake.
D)Nobody is asleep.

Accepted Answer

The negation of "Everyone is asleep" is "Not everyone is asleep," meaning there is at least one person who is not asleep.

Quiz 3: Introduction to Logic

Write a negation for the statement. -No fifth graders play soccer.

Convert the symbolic compound statement into words. -p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: $p \wedge q$

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim does not play football and Michael plays basketball.

Write a negation for the statement. -Some people don't like walking.

Write a negation for the statement. -Not all people like football.

Convert the symbolic compound statement into words. -p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston." Translate the following compound statement into words: $p \vee q$

Convert the symbolic compound statement into words. -p represents the statement "It's Monday." q represents the statement "It's raining today." Translate the following compound statement into words: $\sim \mathrm { p } \vee \sim \mathrm { q }$

Write a negation for the statement. -She earns more than me.

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Neither Jim plays football nor Michael plays basketball.

Write a negation of the inequality. Do not use a slash symbol. - $x < 5$

Convert the symbolic compound statement into words. -p represents the statement : "Students are happy." q represents the statement: "Teachers are happy." Translate the following compound statement into words: $\sim ( p \vee \sim q )$

Write a negation of the inequality. Do not use a slash symbol. - $x \leq 12$

Write a negation for the statement. -Some athletes are musicians.

Write a negation of the inequality. Do not use a slash symbol. - $x > 69$

Convert the symbolic compound statement into words. -p represents the statement: " $x < 1$ " q represents the statement: " $y > 1$ " Translate the following compound statement into words: $\mathrm { p } \vee\sim \mathrm { q }$

Convert the symbolic compound statement into words. -p represents the statement "It's Monday." q represents the statement "It's raining today." Translate the following compound statement into words: $\sim p \wedge \sim q$

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim does not play football and Michael does not play basketball.

Write a negation of the inequality. Do not use a slash symbol. - $x \geq - 50$

Convert the symbolic compound statement into words. -p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: $\sim p$

Write a negation for the statement. -Everyone is asleep.

Quiz 3: Introduction to Logic

Write a negation for the statement. -No fifth graders play soccer.

Convert the symbolic compound statement into words. -p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: p∧qp \wedge qp∧q

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim does not play football and Michael plays basketball.

Write a negation for the statement. -Some people don't like walking.

Write a negation for the statement. -Not all people like football.

Convert the symbolic compound statement into words. -p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston." Translate the following compound statement into words: p∨qp \vee qp∨q

Convert the symbolic compound statement into words. -p represents the statement "It's Monday." q represents the statement "It's raining today." Translate the following compound statement into words: ∼p∨∼q\sim \mathrm { p } \vee \sim \mathrm { q }∼p∨∼q

Write a negation for the statement. -She earns more than me.

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Neither Jim plays football nor Michael plays basketball.

Write a negation of the inequality. Do not use a slash symbol. - x<5x < 5x<5

Convert the symbolic compound statement into words. -p represents the statement : "Students are happy." q represents the statement: "Teachers are happy." Translate the following compound statement into words: ∼(p∨∼q) \sim ( p \vee \sim q ) ∼(p∨∼q)

Write a negation of the inequality. Do not use a slash symbol. - x≤12x \leq 12x≤12