Jul 26, 2011 Posted on Jul 26, 2011 | Comments Off on Lesson 4 Tweet

Fundamentals of Advanced Mathematics Lesson 4: Contrapositive and Equivalence

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Problems

• 1.2.1 Identify the antecedent and the consequent for each of the following conditional sentences. Assume that a, b, and f represent some fixed sequence, integer, or function, respectively.
  (Solution, sausagegobbler )

• 1.2.2 Write the converse and contrapositive of each conditional sentence in exercise 1
  (Solution not available yet; Solve it!)

• 1.2.3 Identify the antecedent and consequent for each conditional sentence in the following statements from this book.
  (Solution not available yet; Solve it!)

• 1.2.4 Which of the following conditional sentences are true?
  (Solution, sausagegobbler, jamesdthomson)

• 1.2.5 Which of the following are true?
  (Solution, sausagegobbler)

• 1.2.6 Make truth tables for these propositional forms.
  (Solution not available yet; Solve it!)

• 1.2.7 Prove Theorem 1.2 by constructing truth tables for each equivalence.
  (Solution not available yet; Solve it!)

• 1.2.8 Rewrite each of the following sentences using logical connectives. Assume that each symbol f, n, x, S, B represents some fixed object.
  (Solution not available yet; Solve it!)

• 1.2.9 Show that the following pairs of statements are equivalent.
  (Solution not available yet; Solve it!)

• 1.2.10 Give, if possible, an example of a true conditional sentence for which
  (Solution not available yet; Solve it!)

• 1.2.11 Give, if possible, an example of a false conditional sentence for which
  (Solution not available yet; Solve it!)

• 1.2.12 Give the converse and contrapositive of each sentence of exercise 8(a), (b), (c), and (d). Tell whether each converse and contrapositive is true or false.
  (Solution not available yet; Solve it!)

• 1.2.13 The inverse, or opposite, of the conditional sentence P?Q is ¬P?¬Q.
  (Solution not available yet; Solve it!)

• 1.2.14 Determine whether each of the following is a tautology, a contradiction, or neither.
  (Solution not available yet; Solve it!)