Introduction to Logic

Stefan Waner and Steven R. Costenoble

Exercises for Section 3:
The Conditional and the Biconditional

Answers To see an answer to any odd-numbered exercise, just click on the exercise number.

Determine the truth value (if it exists) of each of the following statements.

Construct the truth table for each of the following statements, and indicate which (if any) are tautologies or contradictions.

Use truth tables to demonstrate the following equivalences.

Give the contrapositive and converse of each of the following statements, phrasing your answers in words:

Express each of the following statements in equivalent disjunctive form.

Translate the following into compound statements utilizing either the conditional or the biconditional, and using "p" for the statement "I am Julius Caesar" and "q" for the statement "You are Brutus"

Communication and Reasoning Exercises

71. Give an example of an instance where pq means that q causes p.

72. Complete the following. If pq, then its convese,, is the statement thatand (is/is not) logically equivalent to pq.

73. Complete the following sentence. If both pq and its are true, then the biconditional, , is.

74. If B is a tautology, why is AB also a tautology, regardless of A?

75. If A is a contradiction, why is AB a tautology, regardless of B?

76. If A is a tautology and B is a contradiciton, what can you say about AB?

77. If A and B are both contradictions, what can you say about AB?

78. Give an instance of a biconditional pq where neither p nor q causes the other.

Last Updated: September, 2001
Copyright © 1996 StefanWaner and Steven R. Costenoble

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