Challenge Exercises for Mathematical Logic

Directions: Read each question below. Create a truth table to help you answer each question. The answer choices provided correspond to the last column of the truth table for a given problem. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1.   What are the truth values for this statement?   ~pq
 
{T, F, F, F}
{F, T, T, T}
{F, F, T, F}
None of the above.

RESULTS BOX:  
2.   What are the truth values for this statement?   p~q
 
{T, T, F, T}
{F, F, T, F}
{F, T, F, F}
None of the above.

RESULTS BOX:  
3.   What are the truth values for this statement?   ~ab
 
{F, T, T, F}
{T, T, T, F}
{T, F, T, T}
None of the above.

RESULTS BOX:  
4.   What are the truth values for this statement?   a~b
 
{F, T, T, T}
{T, F, T, F}
{T, T, T, F}
None of the above.

RESULTS BOX:  
5.   Choose the word or phrase that best completes this sentence:   The statements in problems 3 and 4 are ____________.
 
Logically equivalent
Biconditional
Tautologies
None of the above.

RESULTS BOX:  
6.   What are the truth values for this statement?   ~qp
 
{F, T, T, T}
{T, F, T, F}
{T, T, T, F}
None of the above.

RESULTS BOX:  
7.   Which statement below is logically equivalent to the statement in problem 6?
 
pq
pq
pq
None of the above.

RESULTS BOX:  
8.   What are the truth values for this statement?   ~r~(rs)
 
{T, T, T, T}
{F, F, F, F}
{T, T, T, F}
None of the above.

RESULTS BOX: 
9.   What are the truth values for this statement?   (~qp)(pq)
 
{F, T, T, T}
{T, T, T, F}
{T, T, T, T}
None of the above.

RESULTS BOX:  
10.   Choose the word or phrase that best completes this sentence:   The statements given in problems 8 and 9 are _______.
 
Conjunctions
Tautologies
Triconditionals
None of the above.

RESULTS BOX: