Definition of Compound Statement

[wishyouwell]

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!

 

[WWGD]

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).

 

[Mark44]

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.

 

[symbolipoint]

Two sentences combined with the conjunction OR

 

[HallsofIvy]

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.)

 

[Mark44]

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...