Practice Exercises for Mathematical Logic

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1.   
 p   q  ~p pq pq pq
T T T T T
T F F T F
F T T F T
F F T F F
  
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2.   
 p   q   ~q pq (pq)~q
T F T F
T F F T
F T F T
F F T F
  
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3.   
 x   y  xy yx (xy)(yx) xy
T T T T T
T F F F F
F T T F F
F F T T T
  
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4.   
Which of the following statements from problem 3 is conditional?
x
y
xy
None of the above.

RESULTS BOX:
    
5.   
Which of the following statements from problem 3 is biconditional?
xy
yx
xy
None of the above.

RESULTS BOX:
    

 

 

 
6.   
 a   b  ab (ab)a [(ab)a]b
T T T T
T F F T
F T T T
F F T F
  
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7.   
Choose the word that best completes this sentence:
The statement in the last column of the truth table in problem 6 is a ____________.
Biconditional
Tautology
Disjunction
None of the above.

RESULTS BOX:
    

 

 
8.   
 p   q  ~q p~q pq ~(pq) (p~q)[~(pq)]
T T F T F T
T F T T T T
F T T T F T
F F T T F T
  
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9.   
Which two statements from problem 8 are logically equivalent?
p~q and pq
pq and ~(pq)
p~q and ~(pq)
None of the above.

RESULTS BOX:
    
10.  
Choose the word that best completes this sentence:
The ____________ of two equivalent statements always yields a tautology.
Biconditional
Conjunction
Negation
All of the above.

RESULTS BOX:
    

 

Lessons on Symbolic Logic
Negation
Conjunction
Disjunction
Conditional
Compound
Biconditional
Tautologies
Equivalence
Practice Exercises
Challenge Exercises
Solutions

IXL