Concept explainers
(a)
To find: Whether
(a)
Answer to Problem 16E
Tautology
Explanation of Solution
Concept Used:
If the propositions
In a truth table, if the given expression holds true for all values then it is a tautology, if it holds false for all values then it is a contradiction, else it is neither.
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(b)
To find: Whether
(b)
Answer to Problem 16E
Tautology
Explanation of Solution
Concept Used:
If the propositions
If at least one of
If the propositions
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(c)
To find: Whether
(c)
Answer to Problem 16E
Contradiction
Explanation of Solution
Concept Used:
If the propositions
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(d)
To find: Whether
(d)
Answer to Problem 16E
Nether
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(e)
To find: Whether
(e)
Answer to Problem 16E
Tautology
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(f)
To find: Whether
(f)
Answer to Problem 16E
Neither
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(g)
To find: Whether
(g)
Answer to Problem 16E
Contradiction
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(h)
To find: Whether
(h)
Answer to Problem 16E
Tautology
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(i)
To find: Whether
(i)
Answer to Problem 16E
Contradiction
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(j)
To find: Whether
(j)
Answer to Problem 16E
Neither
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(k)
To find: Whether
(k)
Answer to Problem 16E
Tautology
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
(l)
To find: Whether
(l)
Answer to Problem 16E
Neither
Explanation of Solution
Calculation:
Below is the truth table for the given expression.
The given expression holds true for all values, therefore
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Chapter 1 Solutions
A Transition to Advanced Mathematics
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,