Is Compound statement always a proposition?

"Compound statements are statements using two or more logic operations. Creating a truth table is a systematic way of determining when a compound statement is true and when it is false. "

I read those lines somewhere. Were those correct? If these are correct , Can you please let me know whether compound statement is considered as statement or not. Because as far as the definition of statement or proposition is concerned , statement is always associated with a unique truth value. But compound statement's truth value may vary. So compound statement is not necessarily a statement.

E.g - If $x^2 - y^2 = 0$ then $x = y$.

It will be true when $2,2$ but false when $2, -2$.so the truth value is varying.

Can you please correct me if I am wrong anywhere?

• I really can not understand. Can you please elaborate. I have given one new example. Can you please explain why that compound statement is a statement? – cmi Feb 24 '18 at 17:05
• The definition you quote say "Compound statements are statements ..." – Hagen von Eitzen Feb 24 '18 at 17:14
• Sorry... but you have changed your example :-) – Mauro ALLEGRANZA Feb 24 '18 at 17:19

Yes, it is.

The quoted sentence means that the truth value of the compound statement is uniquely determined by the truth values of the composing statements through the truth table for the connectives.

Consider the example:

"If it rains, then the meeting will be postponed".

If "It rains" is true and "The meeting will be postponed" is false, then the compound statement is false.

If we consider an open formula, like e.g. $x=2$, it is not a statement, because it lacks a definite truth value.

Its truth value will be determined by the value assigned to the variable $x$: if we assign to $x$ the value $2$, the resulting statement is true. If we assign to $x$ the value $1$, the statement is false.

• can u please explain that example? It seems more complicated. I am still having hard time to see that example as a statement. @Mauro ALLEGRANZA – cmi Feb 24 '18 at 17:57