Computer Science: An Overview (12th Edition)
12th Edition
ISBN: 9780133760064
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Chapter 6.7, Problem 2QE
Program Plan Intro
Inconsistent statement:
A system of statement is inconsistent if all the statements are not true at the same time. The statements in inconsistent system of statements are self-contradictory in nature.
Consistent statements:
In consistent system of statements all statement must be true at the same time.
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Determine the validity of the ff. proof:
Theorem: "the sum of any two rational numbers is a rational number"
Proof:
"Proof: Suppose r and s are rational numbers. By
definition of rational, r = a/b for some integers
a and b with b + 0, and s = a/b for some integers
a and b with b + 0. Then
2a
a
r+s ==+
b b
a
- =
b
Let p = 2a. Then p is an integer since it is a prod-
uct of integers. Hence r+s = p/b, where p and b
are integers and b + 0. Thus r+ s is a rational
number by definition of rational. This is what was
to be shown."
Maybe
O Yes, it is valid
Insufficient information to find the answer
Not valid
Can we go back to number four
Rewrite the following statement formally. Use variables and include both quantifiers ∀ and ∃ in your answer. Every even integer greater than 2 can be written as a sum of two prime numbers.
Chapter 6 Solutions
Computer Science: An Overview (12th Edition)
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