# Practice Exercises for Mathematical Logic

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: