Question 1

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-Trevor wanted to attend the meeting, but he had to go to the party.
A) Compound; negation; $\sim$ 
B) Compound; conjunction; $\wedge$
C) Compound; disjunction; $\vee$
D) Simple statement

Accepted Answer

The statement is a compound statement because it combines two simple statements ("Trevor wanted to attend the meeting" and "he had to go to the party") using the conjunction "but," which is represented by the symbol $\wedge$.

Question 2

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 does not play basketball. 
A) $p \vee q$
B) $\sim \mathrm { p } \vee \sim \mathrm { q }$
C) $p \wedge q$
D) $\sim \mathrm { p } \wedge \sim \mathrm { q }$

Accepted Answer

The statement "Jim does not play football and Michael does not play basketball" negates both p and q and joins them with "and", which is represented by $\sim p \wedge \sim q$.

Question 3

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The apartment is rented or it is available.
A) Compound; conjunction; $\wedge$
B) Compound; disjunction; $\vee$
C) Compound; biconditional; $\leftrightarrow$
D) Compound; conditional; $\rightarrow$

Accepted Answer

The statement is a compound statement because it is made up of two simple statements connected by "or," making it a disjunction, represented by the symbol $\vee$.

Question 4

Write a negation of the statement.
-All dinosaurs were carnivores.
A) All dinosaurs were not carnivores.
B) Some dinosaurs were not carnivores.
C) No dinosaurs were carnivores.
D) Some dinosaurs were carnivores.

Accepted Answer

The negation of "All dinosaurs were carnivores" is "Some dinosaurs were not carnivores," which means at least one dinosaur was not a carnivore, directly contradicting the original statement.

Question 5

Write a negation of the statement.
-Everyone is asleep.
A) Everyone is not asleep.
B) None are asleep.
C) Everyone is awake.
D) Not everyone is asleep.

Accepted Answer

The correct negation of "Everyone is asleep" is "Not everyone is asleep," which means there is at least one person who is not asleep. This does not necessarily mean that everyone is awake, just that the original statement is not true for everyone.

Question 6

Write a negation of the statement.
-Some citizens obey traffic laws.
A) All citizens obey traffic laws.
B) No citizens do not obey traffic laws.
C) Some citizens do not obey traffic laws.
D) No citizens obey traffic laws.

Accepted Answer

The answer of Write a negation of the statement.
-Some citizens...

Question 7

Write a negation of the statement.
-No fifth graders play soccer.
A) Some fifth graders play soccer.
B) Everybody plays soccer.
C) Fifth graders play soccer.
D) Everybody does not play soccer.

Accepted Answer

The negation of "No fifth graders play soccer" is "Some fifth graders play soccer," which directly contradicts the original statement by asserting that there is at least one fifth grader who plays soccer.

Question 8

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

Accepted Answer

The negation of "She earns more than me" is "She does not earn more than me," which directly contradicts the original statement without specifying how their earnings compare beyond that.

Question 9

Write a negation of the statement.
-All squares are parallelograms.
A) Some squares are parallelograms.
B) Some squares are not parallelograms.
C) All squares are not parallelograms.
D) No squares are parallelograms.

Accepted Answer

The negation of "All squares are parallelograms" is "Some squares are not parallelograms," because it directly contradicts the original statement by asserting that there is at least one square that is not a parallelogram.

Question 10

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-If you forget to bring the book back to the library, you will have to pay a fine.
A) Simple statement
B) Compound; biconditional; $\leftrightarrow$
C) Compound; conditional; →
D) Compound; conjunction; $\wedge$

Accepted Answer

The statement is a compound statement because it consists of two parts: "If you forget to bring the book back to the library" and "you will have to pay a fine." It is a conditional statement because the second part of the statement happens on the condition that the first part happens. The symbol for a conditional statement is →.

Question 11

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

Accepted Answer

The statement "Neither Jim plays football nor Michael plays basketball" negates the entire statement that either Jim plays football or Michael plays basketball, which is symbolically represented as $\sim ( p \vee q )$.

Question 12

Write a negation of the statement.
-Some athletes are musicians.
A) All athletes are musicians.
B) All athletes are not musicians.
C) Some athletes are not musicians.
D) No athletes are musicians.

Accepted Answer

The negation of "Some athletes are musicians" is "No athletes are musicians," as it directly contradicts the existence of any athlete who is a musician.

Question 13

Write a negation of the statement.
-Some photographs are not displayed at this exhibition.
A) No photographs are displayed at this exhibition.
B) Some photographs are displayed at this exhibition.
C) All photographs are displayed at this exhibition.
D) All photographs are not displayed at this exhibition.

Accepted Answer

The negation of "Some photographs are not displayed at this exhibition" is "All photographs are displayed at this exhibition," because it directly contradicts the original statement by asserting that there are no exceptions to the photographs being displayed.

Question 14

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The animal is a mammal if and only if it nurses its young.
A) Compound; disjunction; $\vee$
B) Compound; biconditional; $\leftrightarrow$
C) Compound; conditional; $\rightarrow$
D) Compound; negation; $\sim$

Accepted Answer

The statement is a compound statement because it connects two simpler statements ("The animal is a mammal" and "it nurses its young") with "if and only if," which is a biconditional logical connector, represented by the symbol $\leftrightarrow$.

Question 15

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The team leader has decided to take a vacation.
A) Compound; conditional; $\rightarrow$
B) Compound; negation; $\sim$ 
C) Compound; conjunction; $\wedge$
D) Simple statement

Accepted Answer

The statement "The team leader has decided to take a vacation" cannot be broken down into simpler statements connected by logical operators, making it a simple statement.

Question 16

Write a negation of the statement.
-Not all people like football.
A) Some people do not like football.
B) Some people like football.
C) All people like football.
D) All people do not 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 17

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-It is false that whales are fish and bats are birds.
A) Compound; biconditional; $\leftrightarrow$
B) Compound; disjunction; $\vee$
C) Compound; negation;$\sim$ 
D) Compound; conjunction; $\wedge$

Accepted Answer

This statement is a compound statement because it involves a negation ($\sim$) of a conjunction ($\wedge$) statement ("whales are fish and bats are birds").

Question 18

Write a negation of the statement.
-Some people donʹt like walking.
A) Some people like walking.
B) All people like walking.
C) Nobody likes walking.
D) Some people donʹt like driving.

Accepted Answer

The negation of "Some people donʹt like walking" is "All people like walking," because it directly contradicts the original statement by asserting that there are no exceptions to people liking walking.

Question 19

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The clown is not amusing.
A) Compound; disjunction; $\vee$
B) Simple statement, negation; $\sim$ 
C) Simple statement
D) Compound; conjunction; $\wedge$

Accepted Answer

The statement is simple but contains a negation, indicated by "not amusing," which can be symbolized using $\sim$.

Question 20

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The car is in the garage and the bicycle is in the driveway. 
A) Compound; disjunction; $v$
B) Compound; conditional; $\rightarrow$
C) Compound; biconditional; $\leftrightarrow$
D) Compound; conjunction; $\wedge$

Accepted Answer

The statement is a compound statement because it combines two simple statements ("The car is in the garage" and "the bicycle is in the driveway") using the conjunction "and", which is represented by the symbol $\wedge$.

Quiz 3: Logic

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 does not play basketball.

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The apartment is rented or it is available.

Write a negation of the statement. -All dinosaurs were carnivores.

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

Write a negation of the statement. -Some citizens obey traffic laws.

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

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

Write a negation of the statement. -All squares are parallelograms.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Neither Jim plays football nor Michael plays basketball.

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

Write a negation of the statement. -Some photographs are not displayed at this exhibition.

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The team leader has decided to take a vacation.

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

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -It is false that whales are fish and bats are birds.

Write a negation of the statement. -Some people donʹt like walking.

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The clown is not amusing.