15. Even though we will normally use "implies" and "if ..., then..." to describe implication, other word orders and phrases often arise in practice, as in the examples below. Let p, q, and r be the propositions p= "the flag is set," q="1=0," r="subroutine S is completed." Translate each of the following propositions into sym- bols, using the letters p, q, and r and the logical connec- tives. (a) If the flag is set, then I = 0. (b) Subroutine S is completed if the flag is set. (c) The flag is set if subroutine S is not completed.
15. Even though we will normally use "implies" and "if ..., then..." to describe implication, other word orders and phrases often arise in practice, as in the examples below. Let p, q, and r be the propositions p= "the flag is set," q="1=0," r="subroutine S is completed." Translate each of the following propositions into sym- bols, using the letters p, q, and r and the logical connec- tives. (a) If the flag is set, then I = 0. (b) Subroutine S is completed if the flag is set. (c) The flag is set if subroutine S is not completed.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:15. Even though we will normally use “implies” and “if …..,
then... "to describe implication, other word orders and
phrases often arise in practice, as in the examples below.
Let p, q, and r be the propositions
p= "the flag is set,"
q="1=0,"
r = "subroutine S is completed."
Translate each of the following propositions into sym-
bols, using the letters p, q, and r and the logical connec-
tives.
(a) If the flag is set, then I = 0.
(b) Subroutine S is completed if the flag is set.
(c) The flag is set if subroutine S is not completed.
(d) Whenever I = 0, the flag is set.
(e) Subroutine S is completed only if I = 0.
(f) Subroutine S is completed only if I = 0 or the flag
is set.
Note the ambiguity in part (f); there are two different
answers, each with its own claim to validity. Would
punctuation help?
Expert Solution
Step 1: Given.
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Given: 15. are the propositions "The flag is set", "" and "subroutine is completed".
To translate: Each of the following propositions into symbols using the letters and the logical connectives.
(a) If the flag is set, then .
(b) Subroutine is completed if the flag is set.
(c) The flag is set if subroutine is not completed.
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