Concept explainers
Construct a truth table and determine whether the statement is a tautology.
Answer to Problem 17E
The given statement is a tautology.
Explanation of Solution
Given information :
The given statements is
Calculation :
A compound statement that is true for all truth values of its component statement is called a tautology.
The truth table of
Column 4 is constructed by using disjunction with column 1 and 2.
Column 5 is constructed by using conjunction with column 3 and 4.
Column 6 is constructed by using conjunction with column 3 and 1.
Column 7 is constructed by using conjunction with column 3 and 2.
Column 8 is constructed by using disjunction with column 6 and 7.
Column 9 is constructed by using equivalence with column 5 and 8.
From the above truth table:
Since, the given statement is true for all truth values of its component statement, therefore it is a tautology.
Hence,
The given statement is a tautology.
Chapter 2 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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