Working with
Logic

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Answer the following questions which deal with logical reasoning.

1.   "A square has 4 equal sides."
What is the truth value of the negation of this sentence?
 

 

 

2. What is the truth value of the statement
"2 + 4 = 6  and  9 is a prime number."?

 

 

3. What is the truth value of the statement 
"Triangles have 3 sides or squares have 3 sides."?

 

 

4. What is the truth value of the statement
"2 is even and 4 is odd."?

 

 

5. What is the truth value of the statement 
"If dogs bark, then horses quack."?

 

 

6. What is the truth value of the statement
"If horses quack, then cows moo."?

 

 

 

7. The sentence "If _____, then 4 + 3 = 7." is true. 
Which of the following statements could be used to fill the blank?

a.  6/3 = 2
b.  8/4  = 3
c.  both a and b could be used

 

 

8. What is the truth value of the sentence
"No triangle has three sides or all triangles have three sides."
?

 

 

9. The sentence " _____ if and only if x + x = 3x." is true.  Which of the following statements could be used to fill the blank?

a.  x + x = 2x
b.  2x - x = 2x
c.  both a and b can be used

 

 

10. It is true that Donald has blue eyes and Alice has green eyes. 
What is the truth value of the sentence
"If Donald has green eyes, then Alice has green eyes."?

 

 

 

11. a.  What is the truth value of the sentence
 "May has 31 days and June has 31 days."?

b.  Is the sentence in part 'a' called a conjunction or a disjunction?

 

 

 

 

12. What is the truth value of
"3 is a prime number if and only if a right angle contains exactly 60 degrees."?