# Practice Exercises for Mathematical Logic

1.
 p q ~p p q p q p q T T T T T T F F T F F T T F T F F T F F

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 p q ~q p q (p q) ~q T F T F T F F T F T F T F F T F

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 x y x y y x (x y) (y x) x y T T T T T T F F F F F T T F F F F T T T

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 Which of the following statements from problem 3 is conditional? xyx yNone of the above. RESULTS BOX: 5.
 Which of the following statements from problem 3 is biconditional? x yy xx yNone of the above. RESULTS BOX:

6.
 a b a b (a b) a [(a b) a] b T T T T T F F T F T T T F F T F

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 Choose the word that best completes this sentence: The statement in the last column of the truth table in problem 6 is a ____________. BiconditionalTautologyDisjunctionNone of the above. RESULTS BOX:

8.
 p q ~q p ~q p q ~(p q) (p ~q) [~(p q)] 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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 Which two statements from problem 8 are logically equivalent? p ~q and p qp q and ~(p q)p ~q and ~(p q)None of the above. RESULTS BOX: 10.
 Choose the word that best completes this sentence: The ____________ of two equivalent statements always yields a tautology. BiconditionalConjunctionNegationAll of the above. RESULTS BOX:

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