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Chapter 3: Problem 66

Construct a truth table for each statement. \([(p \vee \sim r) \wedge(q \vee \sim r)] \vee \sim(\sim p \vee r)\)

Short Answer

Expert verified
The truth table will have 8 rows, representing the 8 possible combinations of truth values of p, q, and r. Each row will then have the calculated truth values for each of the subexpressions and the entire expression, based on the truth values of p, q, and r in that row.

Step by step solution

01

Establish the Truth Value Possibilities

Since there are three variables (p, q, r), each of which can take the values true (T) or false (F), there are \(2^3 = 8\) possible combinations of truth values for these variables.
02

Evaluate the Subexpressions

Before evaluating the entire expression, evaluate the value of the sub-expression \((p \vee \sim r)\), \((q \vee \sim r)\), and \(\sim(\sim p \vee r)\) separately for each of the 8 combinations.
03

Evaluate the Entire Expression

Finally, use the results from step 2 to evaluate the truth value of the entire expression \([(p \vee \sim r) \wedge(q \vee \sim r)] \vee \sim(\sim p \vee r)\) for each of the 8 combinations.

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Most popular questions from this chapter

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. Having a college degree is necessary for obtaining a teaching position. You do not obtain a teaching position, so you do not have a college degree.

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