Definition of Compound Statement

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What I can add is that the textbook is incorrect. It is not a compound statement. It is an or statement. And it is a proposition, which is a statement with a truth value.In summary, "Either 1+1=2 or a pencil is a useful tool in neurosurgery" is an example of an "or" statement, with its truth value depending on the truth value of both statements. While it may be seen as a compound statement in sentence or predicate logic, it ultimately falls under general math. The truth value of this statement is true, as "1+1=2" is true and "a pencil is a useful tool in neurosurgery" is false.
  • #1
wishyouwell
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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!
 
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  • #2
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).
 
  • #3
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.
 
  • #4
Two sentences combined with the conjunction OR
 
  • #5
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.)
 
  • #6
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...
 

What is a compound statement?

A compound statement is a logical statement in which two or more simple statements are combined using logical operators such as "and," "or," and "not." This allows for more complex and precise expressions of logic.

What is the purpose of a compound statement?

The purpose of a compound statement is to express a more complex logical relationship between simple statements. It allows for the creation of more sophisticated and precise logical arguments and can help in making decisions based on multiple conditions.

What are the components of a compound statement?

A compound statement consists of two or more simple statements, logical operators, and parentheses to indicate the order of operations. The simple statements can be either true or false, and the logical operators connect them to form a compound statement.

What is the difference between a compound statement and a simple statement?

A simple statement is a basic statement that can be either true or false, while a compound statement is made up of multiple simple statements connected by logical operators. A simple statement is usually a single sentence, while a compound statement can be a combination of multiple sentences.

What is an example of a compound statement?

An example of a compound statement is "If it is raining and I have an umbrella, then I will go for a walk." This statement consists of two simple statements ("it is raining" and "I have an umbrella") connected by the logical operator "and."

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