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Chapter 3: Problem 93

Describe how to set up the eight different true-false combinations for a compound statement consisting of three simple statements.

Short Answer

Expert verified
The eight different true-false combinations for a compound statement consisting of three simple statements are (T, T, T), (T, T, F), (T, F, T), (T, F, F), (F, T, T), (F, T, F), (F, F, T), (F, F, F).

Step by step solution

01

Understanding Simple Statements

First, it is important to realize what a simple statement is. A simple statement is an assertion that could either be true or false but not both. Let's suppose we have three simple statements 'p', 'q', and 'r'.
02

Creation of Truth Table

Now, we create a truth table. A truth table displays all the possible combinations of truth values that the simple statements could take, and descriptions of compound statements based on these values. Since we have three simple statements, and each of them could be either true or false, we will have \(2^3\) or 8 different truth-value combinations to consider.
03

Listing Out All Possible Combinations

The eight different truth-value combinations are as follows in the pattern (p, q, r): (T, T, T), (T, T, F), (T, F, T), (T, F, F), (F, T, T), (F, T, F), (F, F, T), (F, F, F). T stands for 'True' and F stands for 'False'.

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