MATH 3181 Section 001 Fall, 1996

HOMEWORK SET 1

1. Write each statement in symbolic form, letting the statements be:

   

   1. Both Romulus and Remus are studying.
   2. Remus is studying but Romulus is not.
   3. Neither Romulus nor Remus is studying.
   4. Either Romulus is studying or Remus is not.
   5. It is not true that both Romulus and Remus are studying.
   6. Either Romulus or Remus is studying.
   7. It is not true that both Romulus and Remus are not studying.

2. Assume that the statements P and Q in Problem 1 are both true. Which of the compound statements in Problem 1 are then true?

3. Let P be the statement `` The corn is green'' and Q be the statement `` The sky is blue''. Translate the following statements into words.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 

4. Construct truth tables for the following statements.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 

5. Let be defined as `` P or Q but not both,'' and construct a truth table for this connective.

6. 6 Construct truth tables for the following:
   1. 
   2. 
   3. 
   4. 

7. Write the converse, inverse, and contrapositive of each of the following statements.
   1. If a triangle is isosceles, then the sides opposite the congruent angles are congruent.
   2. If x is positive, then .

8. Construct a truth table for

   

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