Question 1

Find a so that the statement is true.

Accepted Answer

A)  7 
B)  4 
C)  5 
D)  6 
E)  0 
A)  7 
B)  4 
C)  5 
D)  6 
E)  0

Question 2

Construct a truth table for the given statement.   ​

Accepted Answer

The answer of Construct a truth table for the given...

Question 3

Fill in the blank with a symbolic statement that follows from the given statement.
Utilities, except for water and garbage, are paid by the tenant. Let
t: You are a tenant.
w: You pay water.
g: You pay garbage.
u: You pay the other utilities.
​

Accepted Answer

The answer of Fill in the blank with a symbolic...

Question 4

Find a so that the statement is true.   a = __________

Accepted Answer

The answer of Find a so that the statement is...

Question 5

I visited a beautiful flower garden yesterday and counted exactly 60 flowers. Each flower was either white or purple, and the flowers were not all the same color. My friend made the following observation: No matter which two flowers you might have picked, at least one was bound to be white. From this can you determine how many were white and how many were purple?
​
__________ white flower(s) and __________ purple flower(s)

Accepted Answer

The answer of I visited a beautiful flower garden yesterday...

Question 6

Translate the sentence into if-then form. All prime numbers greater than 2 are odd numbers.
If it is __________ then it __________.

Accepted Answer

A)  a prime number greater than 2; is an odd number 
B)  an odd number; is a prime number greater than 2 
C)  a prime number greater than 2; is not a prime number greater than 2 
D)  an odd number; may be a prime number greater than 2 
A)  a prime number greater than 2; is an odd number 
B)  an odd number; is a prime number greater than 2 
C)  a prime number greater than 2; is not a prime number greater than 2 
D)  an odd number; may be a prime number greater than 2

Question 7

What does the circuit symbol in the figure mean? ​   ​

Accepted Answer

A)  Battery 
B)  Switch 
C)  AND-gate 
D)  Light 
E)  OR-gate 
A)  Battery 
B)  Switch 
C)  AND-gate 
D)  Light 
E)  OR-gate

Question 8

Find a so that the statement is true.

Accepted Answer

A)  5 
B)  3 
C)  4 
D)  2 
E)  0 
A)  5 
B)  3 
C)  4 
D)  2 
E)  0

Question 9

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin?
​
__________ weighings

Accepted Answer

The answer of Suppose you are given 12 coins, one...

Question 10

Find a so that the statement is true.

Accepted Answer

A)  3 
B)  4 
C)  5 
D)  2 
E)  0 
A)  3 
B)  4 
C)  5 
D)  2 
E)  0

Question 11

Using switches, design a circuit that would find the truth values for the statement. ​   ​       ​

Accepted Answer

A)  c 
B)  b 
C)  a 
A)  c 
B)  b 
C)  a

Question 12

Find a so that the statement is true.   a = __________

Accepted Answer

The answer of Find a so that the statement is...

Question 13

Find a so that the statement is true.

Accepted Answer

A)  2 
B)  3 
C)  0 
D)  5 
E)  4 
A)  2 
B)  3 
C)  0 
D)  5 
E)  4

Question 14

Four boys were playing marbles; their names were Bob, Harry, Iggi, and Alice. One of the boys had 9 marbles, another had 15, and each of the other two had 12. Their ages were 3, 10, 17, and 18, but not respectively. Bob shot before Harry and Alice. Alice was older than the boy with 15 marbles. Harry had fewer than 15 marbles. Alice shot before Harry. Iggi shot after Harry. If Iggi was 10 years old, he did not have 15 marbles. Bob and Alice together had an even number of marbles. The youngest boy was not the one with 15 marbles. If Harry had 12 marbles, he wasn't the youngest. The 10-year-old shot after the 17-year-old. How old was each boy?
__________ was 3, __________ was 10, __________ was 17, __________ was 18

Accepted Answer

Iggi; Harr

Question 15

Determine whether the given compound statement is a tautology. Answer yes or no.
​

Accepted Answer

The answer of Determine whether the given compound statement is...

Question 16

Translate the sentence into if-then form. ​
All useless life is an early death.
​

Accepted Answer

A)  If it is a useless life, then it is not an early death. 
B)  If it is a useless life, then it is an early death. 
C)  If it is an early death, then it is not a useless life. 
D)  If it is an early death, then it may be a useless life. 
E)  If it is an early death, then it is a useless life. 
A)  If it is a useless life, then it is not an early death. 
B)  If it is a useless life, then it is an early death. 
C)  If it is an early death, then it is not a useless life. 
D)  If it is an early death, then it may be a useless life. 
E)  If it is an early death, then it is a useless life.

Question 17

Let p : Prices will rise ; q : Taxes will rise. Translate the following statement into symbols. ​
Prices will not rise, and taxes will not rise.
​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

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 19

Find a so that the statement is true.

Accepted Answer

A)  4 
B)  7 
C)  6 
D)  0 
E)  3 
A)  4 
B)  7 
C)  6 
D)  0 
E)  3

Question 20

Let p: Today is Friday; q: There is homework tonight. Translate the following statement into words.
​   ​
Today __________ Friday __________ there __________ homework tonight.

Accepted Answer

The answer of Let p: Today is Friday; q: There...

Find a so that the statement is true.

Construct a truth table for the given statement.

Fill in the blank with a symbolic statement that follows from the given statement. Utilities, except for water and garbage, are paid by the tenant. Let t: You are a tenant. w: You pay water. g: You pay garbage. u: You pay the other utilities.

Find a so that the statement is true. a = __________

Translate the sentence into if-then form. All prime numbers greater than 2 are odd numbers. If it is then it .

What does the circuit symbol in the figure mean?

Find a so that the statement is true.

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin? __________ weighings

Find a so that the statement is true.

Using switches, design a circuit that would find the truth values for the statement.

Find a so that the statement is true. a = __________

Find a so that the statement is true.

Determine whether the given compound statement is a tautology. Answer yes or no.

Translate the sentence into if-then form. All useless life is an early death.

Let p : Prices will rise ; q : Taxes will rise. Translate the following statement into symbols. Prices will not rise, and taxes will not rise.

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.

Find a so that the statement is true.

Let p: Today is Friday; q: There is homework tonight. Translate the following statement into words. Today Friday there __ homework tonight.

The Nature of Problem Solving

The Nature of Sets

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Measurement

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Mathematical Systems

The Nature of Voting and Apportionment

Filters

Exam 3: The Nature of Logic

Find a so that the statement is true.

Construct a truth table for the given statement. ​

Fill in the blank with a symbolic statement that follows from the given statement. Utilities, except for water and garbage, are paid by the tenant. Let t: You are a tenant. w: You pay water. g: You pay garbage. u: You pay the other utilities. ​

Find a so that the statement is true. a = __________

Translate the sentence into if-then form. All prime numbers greater than 2 are odd numbers. If it is __________ then it __________.

What does the circuit symbol in the figure mean? ​ ​

Find a so that the statement is true.

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin? ​ __________ weighings

Find a so that the statement is true.

Using switches, design a circuit that would find the truth values for the statement. ​ ​ ​

Find a so that the statement is true. a = __________

Find a so that the statement is true.

Determine whether the given compound statement is a tautology. Answer yes or no. ​

Translate the sentence into if-then form. ​ All useless life is an early death. ​

Let p : Prices will rise ; q : Taxes will rise. Translate the following statement into symbols. ​ Prices will not rise, and taxes will not rise. ​

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.

Find a so that the statement is true.

Let p: Today is Friday; q: There is homework tonight. Translate the following statement into words. ​ ​ Today __________ Friday __________ there __________ homework tonight.

The Nature of Problem Solving

The Nature of Sets

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Measurement

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Mathematical Systems

The Nature of Voting and Apportionment

Filters

Construct a truth table for the given statement.

Fill in the blank with a symbolic statement that follows from the given statement. Utilities, except for water and garbage, are paid by the tenant. Let t: You are a tenant. w: You pay water. g: You pay garbage. u: You pay the other utilities.

Translate the sentence into if-then form. All prime numbers greater than 2 are odd numbers. If it is then it .

What does the circuit symbol in the figure mean?

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin? __________ weighings

Using switches, design a circuit that would find the truth values for the statement.

Determine whether the given compound statement is a tautology. Answer yes or no.

Translate the sentence into if-then form. All useless life is an early death.

Let p : Prices will rise ; q : Taxes will rise. Translate the following statement into symbols. Prices will not rise, and taxes will not rise.

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.

Let p: Today is Friday; q: There is homework tonight. Translate the following statement into words. Today Friday there __ homework tonight.