Definition of Compound Statement

  • Context: Undergrad 
  • Thread starter Thread starter wishyouwell
  • Start date Start date
  • Tags Tags
    Definition
Click For Summary

Discussion Overview

The discussion revolves around the definition and truth value of a compound statement, specifically using the example "Either 1+1=2 or a pencil is a useful tool in neurosurgery." Participants explore the nature of compound statements in logic, questioning how truth values are assigned and interpreted.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about the truth value of the compound statement, questioning why it is not considered a non-statement.
  • Others clarify that the truth value of the compound statement depends on the truth values of its components, specifically that "1+1=2" is true and "a pencil is a useful tool in neurosurgery" is presumably false.
  • One participant notes that for the compound statement to be true, at least one of the individual statements must be true, which they assert is the case here.
  • There is a mention of the formal representation of the statement in logical terms, indicating its classification as a well-formed formula (wff) in sentence logic.

Areas of Agreement / Disagreement

Participants generally agree on the truth values of the individual statements, but there is some confusion regarding the classification of the compound statement itself and its interpretation as a non-statement.

Contextual Notes

Some participants reference the context of Real Analysis and its relation to General Math, indicating a potential overlap in the subject matter that may affect the discussion.

wishyouwell
Messages
6
Reaction score
0
Hello,

In my Real Analysis textbook (Schramm) they say that an example of compound statement would be "Either 1+1=2 or a pencil is a useful tool in neurosurgery." I was wondering why this isn't a non-statement since I don't see where the truth value of it would be. Thanks!
 
Physics news on Phys.org
wishyouwell said:
Hello,

In my Real Analysis textbook (Schramm) they say that an example of compound statement would be "Either 1+1=2 or a pencil is a useful tool in neurosurgery." I was wondering why this isn't a non-statement since I don't see where the truth value of it would be. Thanks!
It is ultimately an "or" statement and its truth value depends on the truth value of both " Either 1+1=2" and " a pencil is a useful tool in neurosurgery" . If seen as a wff in sentence logic , it can be transcribed as " A or B" , then compound (using A,B) similar in Predicate Logic ( more precisely, FOL).
 
wishyouwell said:
Hello,

In my Real Analysis textbook (Schramm) they say that an example of compound statement would be "Either 1+1=2 or a pencil is a useful tool in neurosurgery." I was wondering why this isn't a non-statement since I don't see where the truth value of it would be. Thanks!
The idea here, with either ... or, is that exactly one of the two statements must be true for the compound statement to be true. In this case 1 + 1 = 2 is a true statement, but (presumably) "a pencil is a useful tool in neurosurgery" is false. Hence the compound statement is true.

This problem may have come from an analysis book, but it really falls under General Math, so I moved this thread.
 
Two sentences combined with the conjunction OR
 
wishyouwell said:
Hello,

In my Real Analysis textbook (Schramm) they say that an example of compound statement would be "Either 1+1=2 or a pencil is a useful tool in neurosurgery." I was wondering why this isn't a non-statement since I don't see where the truth value of it would be. Thanks!
You don't see the truth value? "1+ 1= 2" is true and "a pencil is a useful tool in neurosurgery" is false so the truth value of this statement I "true".
("A or B" is false only when A and B are both false. In all other cases its true.)
 
HallsofIvy said:
You don't see the truth value? "1+ 1= 2" is true and "a pencil is a useful tool in neurosurgery" is false so the truth value of this statement I "true".
That's what I said in post #3...
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 39 ·
2
Replies
39
Views
5K
  • · Replies 21 ·
Replies
21
Views
4K