Concept explainers
NOW TRY THIS
a. Use truth tables to prove Theorem
b. Write a sentence showing the use of De Morgan’s second law in everyday language.
c.
(a)
To prove:
The second De Morgan’s Law for Logic using truth tables.
Answer to Problem 1NT
Solution:
So, the required answer is
T | T | F | F | T | F | F |
T | F | F | T | T | F | F |
F | T | T | F | T | F | F |
F | F | T | T | F | T | T |
Explanation of Solution
Given:
The second De Morgan’s Law for Logic
Approach:
The second De Morgan’s Law for Logic
Calculation:
Hence, the truth table is
T | T | F | F | T | F | F |
T | F | F | T | T | F | F |
F | T | T | F | T | F | F |
F | F | T | T | F | T | T |
(b)
To explain:
The use of De Morgan’s Second Law in everyday language.
Answer to Problem 1NT
Solution:
Let p be “I go the school” and q be “I write a letter”. De Morgan’s Second law of logic might be interpreted as “It is not the case that I go to the school or I write a letter,” has the same meaning as “I do not go the school and I do not write a letter.”
Explanation of Solution
Given:
The second De Morgan’s Law for Logic
Approach:
Let p be “I go the school” and q be “I write a letter”. De Morgan’s Second law of logic might be interpreted as “It is not the case that I go to the school or I write a letter” has the same meaning as “I do not go the school and I do not write a letter.”
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Chapter 2 Solutions
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