Question 1

Write the negation of the statement.
It is not true that the bus is yellow

Accepted Answer

Negating the statement "It is not true that the bus is yellow" results in affirming the opposite, which is "The bus is yellow."

Question 2

Write the negation of the statement.
At least one platypus has been to the arctic.

Accepted Answer

The negation of "at least one" is "none." Therefore, "No platypus has been to the arctic" is the best choice for the negation of the statement. The negation of "at least one" is "none." Therefore, the statement "no platypus has been to the arctic" is the negation of the original statement.

Question 3

Let p = "My homework is finished." Write the following statement in symbols.
My homework is not finished.

Accepted Answer

The answer of Let p = "My homework is finished."...

Question 4

Classify each statement as simple or compound.
I. Jeff's brother is two years old.
Ii. I am going to get a dog or a cat.
Iii. 4 + 1 = 4
Iv. 2 × 0 = 0

Accepted Answer

I. Simple sentence with one subject and one predicate.
II. Compound sentence with two options joined by the coordinating conjunction "or".
III. Simple sentence with a mathematical equation.
IV. Simple sentence with a mathematical equation. I. Simple sentence (subject: Jeff's brother, verb: is, complement: two years old)
II. Compound sentence (two independent clauses joined by the coordinating conjunction "or")
III. Simple sentence (statement of fact with no additional clauses)
IV. Simple sentence (statement of fact with no additional clauses)

Question 5

State whether the sentence is a statement or not.
Close the door.

Accepted Answer

The answer of State whether the sentence is a statement...

Question 6

Determine whether each sentence is a statement or not.
I. He has blond hair.
Ii. He is not home.
Iii. The sky is brown.
Iv. Are you going to try again?

Accepted Answer

- I. "He has blond hair." - statement
- II. "He is not home." - statement
- III. "The sky is brown." - not a statement (factually incorrect)
- IV. "Are you going to try again?" - not a statement (question)

Question 7

Which of the following is a simple statement?

Accepted Answer

Option C is a simple statement as it states a fact that can be proven true or false. Options A, B, and D are compound statements as they contain more than one piece of information connected by conjunctions or conditional statements. Option C is a simple statement because it makes a clear assertion that can be either true or false. Option A is a compound statement as it involves two assertions. Option B is a conditional statement and Option D is a negation.

Question 8

Identify the quantifier in the statement as either universal or existential.
There is a hair in my soup.

Accepted Answer

The quantifier in the statement is "a", which indicates an indefinite singular noun, making it existential. The quantifier "there is" indicates an existential statement, as it implies the existence of at least one instance of the object being referred to (in this case, a hair in the soup).

Question 9

Decide whether each statement is simple or compound.
i. If you win the next round, you will be a finalist.
ii. She is not feeling well.
iii. 7 + 2 = 14
iv. He is taking history and economics.

Accepted Answer

The answer of Decide whether each statement is simple or...

Question 10

Let p = "Daphne speaks Spanish." Let q = "Daphne speaks French." Write the following statement in
symbols.
Daphne speaks Spanish, or Daphne does not speak French.

Accepted Answer

The answer of Let p = "Daphne speaks Spanish." Let...

Question 11

Decide if the statement is simple or compound.
I will go with you if and only if we are on time.

Accepted Answer

The answer of Decide if the statement is simple or...

Question 12

Let p = "Steve has a cat." Let q = "Steve has a dog." Write the following statement in symbols.
Steve does not have a cat, and Steve does not have a dog.

Accepted Answer

The answer of Let p = "Steve has a cat."...

Question 13

Write the negation of the statement.
The dog is spotted.

Accepted Answer

The answer of Write the negation of the statement.
The dog...

Question 14

Let p = "Ed plays the guitar." Let q = "Ed plays the piano." Write the following statement in symbols.
It is not true that Ed does not play the guitar or Ed does not play the piano.

Accepted Answer

The answer of Let p = "Ed plays the guitar."...

Question 15

Identify the quantifier in the statement as universal or existential. Then write the negation of the statement.
Some millionaires are illiterate.

Accepted Answer

The original statement "Some millionaires are illiterate" is existential because it claims the existence of at least one millionaire who is illiterate. The negation flips the existence claim to state that no such individuals exist, hence "All millionaires are literate."

Question 16

Identify the statement as a conjunction, disjunction, conditional, or biconditional.
If Raffi misses the goal, then we will lose the game.

Accepted Answer

The statement is a conditional because it presents a cause-and-effect relationship between Raffi missing the goal and us losing the game. It can be written in the form of "If p, then q", where p is "Raffi misses the goal" and q is "we will lose the game". This statement follows the form of a conditional statement, where the "if" clause (Raffi missing the goal) is the antecedent and the "then" clause (we will lose the game) is the consequent.

Question 17

Identify the statement as a conjunction, disjunction, conditional, or biconditional.
Rory will go to Yale, or she will go to Harvard.

Accepted Answer

This is a disjunction because it presents two options connected by "or." It does not suggest a cause and effect relationship (conditional) or specify that both options must be simultaneously true (biconditional). It also does not connect two statements with "and" (conjunction). This statement is a disjunction because it presents two options (Rory going to Yale or Rory going to Harvard), indicating that at least one of them must be true.

Question 18

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement
in symbols.
If Roberto drives to school, then Paolo bicycles to school.

Accepted Answer

The answer of Let p = "Paolo bicycles to school."...

Question 19

Which sentence is not a statement?

Accepted Answer

A statement is a sentence that declares something that is either true or false. "Stop that." is an imperative sentence, giving a command, rather than stating a fact or claim that can be true or false.

Question 20

Is the following sentence a statement?
Neither Ben nor Alonzo is going camping.

Accepted Answer

The answer of Is the following sentence a statement?
Neither Ben...

Quiz 3: Logic

Write the negation of the statement. It is not true that the bus is yellow

Write the negation of the statement. At least one platypus has been to the arctic.

Let p = "My homework is finished." Write the following statement in symbols. My homework is not finished.

Classify each statement as simple or compound. I. Jeff's brother is two years old. Ii. I am going to get a dog or a cat. Iii. 4 + 1 = 4 Iv. 2 × 0 = 0

State whether the sentence is a statement or not. Close the door.

Determine whether each sentence is a statement or not. I. He has blond hair. Ii. He is not home. Iii. The sky is brown. Iv. Are you going to try again?

Which of the following is a simple statement?

Identify the quantifier in the statement as either universal or existential. There is a hair in my soup.

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. 7 + 2 = 14 iv. He is taking history and economics.

Let p = "Daphne speaks Spanish." Let q = "Daphne speaks French." Write the following statement in symbols. Daphne speaks Spanish, or Daphne does not speak French.

Decide if the statement is simple or compound. I will go with you if and only if we are on time.

Let p = "Steve has a cat." Let q = "Steve has a dog." Write the following statement in symbols. Steve does not have a cat, and Steve does not have a dog.

Write the negation of the statement. The dog is spotted.

Let p = "Ed plays the guitar." Let q = "Ed plays the piano." Write the following statement in symbols. It is not true that Ed does not play the guitar or Ed does not play the piano.

Identify the quantifier in the statement as universal or existential. Then write the negation of the statement. Some millionaires are illiterate.

Identify the statement as a conjunction, disjunction, conditional, or biconditional. If Raffi misses the goal, then we will lose the game.

Identify the statement as a conjunction, disjunction, conditional, or biconditional. Rory will go to Yale, or she will go to Harvard.

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. If Roberto drives to school, then Paolo bicycles to school.

Which sentence is not a statement?

Is the following sentence a statement? Neither Ben nor Alonzo is going camping.