6. Choose the answer that correctly fills in the blank. If a set of statements S is logically inconsistent, then it must be true that (A) more than one member of S is false. (B) the truth of one or more members of S would entail the falsity of some other member of S. (C) every member of S is falsifiable. (D) no member of S is equivalent to any other member.
6. Choose the answer that correctly fills in the blank. If a set of statements S is logically inconsistent, then it must be true that (A) more than one member of S is false. (B) the truth of one or more members of S would entail the falsity of some other member of S. (C) every member of S is falsifiable. (D) no member of S is equivalent to any other member.
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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Question
Transcribed Image Text:**6. Choose the answer that correctly fills in the blank.**
“If a set of statements \( S \) is logically inconsistent, then it must be true that ____________.”
(A) more than one member of \( S \) is false.
(B) the truth of one or more members of \( S \) would entail the falsity of some other member of \( S \).
(C) every member of \( S \) is falsifiable.
(D) no member of \( S \) is equivalent to any other member.
Expert Solution
Step 1
Logical falsity:
Definition: A sentence is logically false if and only if it is not possible for it to be true. Such a sentence is logically false.
Logical consistency:
Definition: A set of sentences is logically consistent if and only if it is possible for all the members of that set to be true.
A consistent set of sentences is a set all of which can be true together. This is not the same as saying that they are all true, merely that it is possible that this is so.
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