Question 1

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning.
​
If  , then  .  Therfore,  .

Accepted Answer

The answer of Determine whether the argument in the problem...

Question 2

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning.
​
All physicists are clever men.
All clever men are rich.
Therefore, all physicists are rich.
​

Accepted Answer

The answer of Determine whether the argument in the problem...

Question 3

Form a valid conclusion, using all the statements for each argument. Give reasons. ​
If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number.
N is not a prime number.

Accepted Answer

Given that if 2 divides a positive integer N and N is greater than 2, then N is not a prime number. The conclusion that N is not a prime number does not necessarily mean that both conditions (2 divides N and N is greater than 2) are false. It means at least one of the conditions for N being a prime number is not met. Therefore, the correct conclusion is that either 2 does not divide N or N is not greater than 2, which matches option D.

Question 4

Form a valid conclusion, using all the statements for each argument. Give reasons.
​
If you learn economics, then you are intelligent.
If you are intelligent, then you understand human nature.
If you __________(learn, don't learn) economics, then you __________ (understand, don't understand) human nature.
__________ (direct, indirect, transitive)

Accepted Answer

The answer of Form a valid conclusion, using all the...

Question 5

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If a² is odd, then a must be odd. a is even. Therefore, a² is even. Assume that if a number is even, then it is not odd.

Accepted Answer

The answer of Determine whether the argument in the problem...

Question 6

Form a valid conclusion, using all the statements for each argument. Give reasons.
​
If we go to the ballet, then we are enlightened.
We are not enlightened.
​
We __________ (go, do not go) to the ballet.
__________ (direct, indirect)

Accepted Answer

The answer of Form a valid conclusion, using all the...

Question 7

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​
All mathematicians are clever men.
All clever men are rich.
Therefore, all mathematicians are rich.
​

Accepted Answer

The argument is valid and uses transitive reasoning. If all mathematicians are clever men, and all clever men are rich, then logically, all mathematicians are rich. This follows the transitive property where if A=B and B=C, then A=C.

Question 8

Form a valid conclusion, using all the statements for each argument. Give reasons. ​
If we win third prize, we will go to the Europe.
If we are ingenious, we will win third prize.
We are ingenious.

Accepted Answer

From the first statement, winning third prize leads to going to Europe. 
From the second statement, being ingenious leads to winning third prize. 
From the third statement, we know that we are ingenious. 
Therefore, using transitive and direct logic, we can conclude that we will win third prize and therefore go to Europe.

Question 9

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning.
​
No students are enthusiastic.
You are a student.
Therefore, you are not enthusiastic.

Accepted Answer

The answer of Determine whether the argument is valid or...

Question 10

Choose a valid conclusion, using all the statements for each argument.
​
If we win third prize, we will go to Europe0.
If we are ingenious, we will win third prize.
We are ingenious.
We will go to Europe0 (transitive and direct)
We won't go to Europe0 (indirect)
We won't win third prize (transitive and direct))

Accepted Answer

The answer of Choose a valid conclusion, using all the...

Question 11

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning.
​
If inherit $1,000, I will buy you a toy .
I inherit $1,000.
Therefore, I will buy you a toy.
​

Accepted Answer

The answer of Determine whether the argument in the problem...

Question 12

Form a valid conclusion, using all the statements for each argument. Give reasons. ​
If you learn mathematics, then you are intelligent.
If you are intelligent, then you understand politics.
​

Accepted Answer

The conclusion in A is valid due to the transitive property: if A implies B (learning mathematics implies intelligence) and B implies C (intelligence implies understanding politics), then A implies C (learning mathematics implies understanding politics).

Question 13

Translate the statement into symbols. ​
To obtain the loan, I must have an income of $85,000 per year. Let
​
P: All provisions of the sale are clearly understood
H: I will buy a new house
K: I must have an income of $85,000 per year
L: Obtaining the loan
S: Smoking
D: Drinking
​

Accepted Answer

The answer of Translate the statement into symbols. ​
To obtain...

Question 14

Determine whether the given compound statement is a tautology. ​
​  ​

Accepted Answer

It is not a tautology as there can be instances where the compound statement is false.

Question 15

Choose a valid conclusion, using all the statements for each argument.
​
Children are illogical.
Nobody is despised who can manage a crocodile0.
Illogical persons are despised.
Children can manage crocodiles 0
Children can't mange crocodiles 0
Everybody can manage crocodiles 0

Accepted Answer

The answer of Choose a valid conclusion, using all the...

Question 16

Explain symbolically what we mean by indirect reasoning.
​
Enter parentheses to indicate the order of operations.
​
Use p and q for a designation of variables.

Accepted Answer

The answer of Explain symbolically what we mean by indirect...

Question 17

Form a valid conclusion, using all the statements for each argument. Give reasons. ​
Children are illogical.
Nobody is despised who can manage a sport car.
Illogical persons are despised.

Accepted Answer

From statement 1, we know that children are illogical. 
From statement 3, we know that illogical persons are despised. 
From statement 2, we know that nobody who can manage a sport car is despised. 
Therefore, if children were able to manage a sport car (choice A or B), they would be despised because they are illogical (statement 1). But this contradicts statement 2. 
Therefore, the only valid conclusion is that children can't manage sport cars (choice C).

Question 18

Form a valid conclusion, using all the statements for each argument. Give reasons. ​
If we go to the theater, then we are enlightened.
We are not enlightened.

Accepted Answer

This is an example of modus tollens, a valid form of argument. If "If P then Q" is true and "Not Q" is true, then "Not P" must also be true. Here, P is "we go to the theater" and Q is "we are enlightened." Given "We are not enlightened" (Not Q), it logically follows that "We do not go to the theater" (Not P).

Question 19

Form a valid conclusion, using all the statements for each argument. Give reasons.
​
If 5 divides a positive integer N and if N is greater than 5, then N is not a prime number.
N is a prime number.
​
5 __________ (divides, does not divide) a positive integer N or __________ (N is a composite number, N is not greater than 5).
__________(direct, indirect)

Accepted Answer

The answer of Form a valid conclusion, using all the...

Question 20

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. No students are enthusiastic.
You are enthusiastic.
Therefore, you are not a student.

Accepted Answer

The argument is valid and uses indirect reasoning (modus tollens). If no students are enthusiastic and you are enthusiastic, then you cannot be a student.

Quiz 3: The Nature of Logic

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If , then . Therfore, .

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. All physicists are clever men. All clever men are rich. Therefore, all physicists are rich.

Form a valid conclusion, using all the statements for each argument. Give reasons. If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number. N is not a prime number.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If a² is odd, then a must be odd. a is even. Therefore, a² is even. Assume that if a number is even, then it is not odd.

Form a valid conclusion, using all the statements for each argument. Give reasons. If we go to the ballet, then we are enlightened. We are not enlightened. We (go, do not go) to the ballet. (direct, indirect)

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. All mathematicians are clever men. All clever men are rich. Therefore, all mathematicians are rich.

Form a valid conclusion, using all the statements for each argument. Give reasons. If we win third prize, we will go to the Europe. If we are ingenious, we will win third prize. We are ingenious.

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. No students are enthusiastic. You are a student. Therefore, you are not enthusiastic.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If inherit $1,000, I will buy you a toy . I inherit $1,000. Therefore, I will buy you a toy.

Form a valid conclusion, using all the statements for each argument. Give reasons. If you learn mathematics, then you are intelligent. If you are intelligent, then you understand politics.

Translate the statement into symbols. To obtain the loan, I must have an income of $85,000 per year. Let P: All provisions of the sale are clearly understood H: I will buy a new house K: I must have an income of $85,000 per year L: Obtaining the loan S: Smoking D: Drinking

Determine whether the given compound statement is a tautology.

Choose a valid conclusion, using all the statements for each argument. Children are illogical. Nobody is despised who can manage a crocodile0. Illogical persons are despised. Children can manage crocodiles 0 Children can't mange crocodiles 0 Everybody can manage crocodiles 0

Explain symbolically what we mean by indirect reasoning. Enter parentheses to indicate the order of operations. Use p and q for a designation of variables.

Form a valid conclusion, using all the statements for each argument. Give reasons. Children are illogical. Nobody is despised who can manage a sport car. Illogical persons are despised.

Form a valid conclusion, using all the statements for each argument. Give reasons. If we go to the theater, then we are enlightened. We are not enlightened.

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. No students are enthusiastic. You are enthusiastic. Therefore, you are not a student.

Quiz 3: The Nature of Logic

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ If , then . Therfore, .

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ All physicists are clever men. All clever men are rich. Therefore, all physicists are rich. ​

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number. N is not a prime number.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ If a2 is odd, then a must be odd. a is even. Therefore, a2 is even. Assume that if a number is even, then it is not odd.

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If we go to the ballet, then we are enlightened. We are not enlightened. ​ We __________ (go, do not go) to the ballet. __________ (direct, indirect)

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ All mathematicians are clever men. All clever men are rich. Therefore, all mathematicians are rich. ​

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If we win third prize, we will go to the Europe. If we are ingenious, we will win third prize. We are ingenious.

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ No students are enthusiastic. You are a student. Therefore, you are not enthusiastic.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ If inherit $1,000, I will buy you a toy . I inherit $1,000. Therefore, I will buy you a toy. ​

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If you learn mathematics, then you are intelligent. If you are intelligent, then you understand politics. ​

Translate the statement into symbols. ​ To obtain the loan, I must have an income of $85,000 per year. Let ​ P: All provisions of the sale are clearly understood H: I will buy a new house K: I must have an income of $85,000 per year L: Obtaining the loan S: Smoking D: Drinking ​

Determine whether the given compound statement is a tautology. ​ ​ ​

Choose a valid conclusion, using all the statements for each argument. ​ Children are illogical. Nobody is despised who can manage a crocodile0. Illogical persons are despised. Children can manage crocodiles 0 Children can't mange crocodiles 0 Everybody can manage crocodiles 0

Explain symbolically what we mean by indirect reasoning. ​ Enter parentheses to indicate the order of operations. ​ Use p and q for a designation of variables.

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ Children are illogical. Nobody is despised who can manage a sport car. Illogical persons are despised.

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If we go to the theater, then we are enlightened. We are not enlightened.

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. No students are enthusiastic. You are enthusiastic. Therefore, you are not a student.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If , then . Therfore, .

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. All physicists are clever men. All clever men are rich. Therefore, all physicists are rich.

Form a valid conclusion, using all the statements for each argument. Give reasons. If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number. N is not a prime number.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If a² is odd, then a must be odd. a is even. Therefore, a² is even. Assume that if a number is even, then it is not odd.

Form a valid conclusion, using all the statements for each argument. Give reasons. If we go to the ballet, then we are enlightened. We are not enlightened. We (go, do not go) to the ballet. (direct, indirect)

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. All mathematicians are clever men. All clever men are rich. Therefore, all mathematicians are rich.

Form a valid conclusion, using all the statements for each argument. Give reasons. If we win third prize, we will go to the Europe. If we are ingenious, we will win third prize. We are ingenious.

Determine whether the argument is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. No students are enthusiastic. You are a student. Therefore, you are not enthusiastic.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. If inherit $1,000, I will buy you a toy . I inherit $1,000. Therefore, I will buy you a toy.

Form a valid conclusion, using all the statements for each argument. Give reasons. If you learn mathematics, then you are intelligent. If you are intelligent, then you understand politics.

Translate the statement into symbols. To obtain the loan, I must have an income of $85,000 per year. Let P: All provisions of the sale are clearly understood H: I will buy a new house K: I must have an income of $85,000 per year L: Obtaining the loan S: Smoking D: Drinking

Determine whether the given compound statement is a tautology.

Choose a valid conclusion, using all the statements for each argument. Children are illogical. Nobody is despised who can manage a crocodile0. Illogical persons are despised. Children can manage crocodiles 0 Children can't mange crocodiles 0 Everybody can manage crocodiles 0

Explain symbolically what we mean by indirect reasoning. Enter parentheses to indicate the order of operations. Use p and q for a designation of variables.

Form a valid conclusion, using all the statements for each argument. Give reasons. Children are illogical. Nobody is despised who can manage a sport car. Illogical persons are despised.

Form a valid conclusion, using all the statements for each argument. Give reasons. If we go to the theater, then we are enlightened. We are not enlightened.