Kemeny, Snell, Thompson
Introduction to Finite Mathematics (Chapter 1)

Coverage: Sections 1, 2, 3, 4, 6, 7.

• Exercises from Section 1: 3, 4, 5, 6, 7.
  Do not use truth tables (even if you can) for 4 and 6.
  • Answer to Exercise 3: (a) p, (b) q, (c) , (d) , (e) ,
    (f) , (g) , (h) .
  • Answer to Exercise 4: Only (b) and (h) are true. The others are false.
• Exercises from Section 2: 2, 6, 7, 8.
  • Answer to Exercise 2: . Can you find another?
  • Answer to Exercise 6: This can be expressed . The truth table is FFFT.
• Exercises from Section 3: 1, 5, 6, 7, 8.
  • Answer to Exercise 1 (a), (b). The three other truth tables are TFTF which is the truth table for q, TFFT which is the truth table for , and TFFF which is the truth table for . Later, the importance of the criterion discussed in (c) should become apparent.
  • Answers to Exercise 7, 8. The statement in 7 is true except when p is false, q is true, r is false, when the statement is false.
    The statement has the same property.
• Exercises from Section 4: 3
  • Answers to (a), (f), (g) are given in the text.
• Exercises from Section 6: 1, 3, 4, 6, 8, 10, 13, 14.
  • Answer to Exercise 1. The first statement has truth table TTTT,, whereas the second has truth table TTTF. implies , whereas does not imply .
  • Answer to Exercise 3 (a). If p is logically true then is true no matter what the truth value of q happens to be.
  • Partial answer to 4 is given in the text.
  • Partial answer to 6. and are equivalent. and are inconsistent.
  • Partial answer to 10 is given in the text.
• Exercises from Section 7: 1, 2, 3, 5, 6, 7, 10, 12, 15.
  • Answers to 1, 2, 3, 6, 7 are given in the text.