Which of These Sentences are Propositions?

[mario99]

Which of these sentences are propositions? What are the truth values of those that are propositions?

(a) Boston is the capital of Massachusetts.
(b) Miami is the capital of Florida.
(c) 2 + 3 = 5.
(d) 5 + 7 = 10.
(e) x + 2 = 11.
(f) Answer this questions.


My attempt.

A proposition is a statement that is true.

(a) The statement is true, so it is a proposition. Its truth value is True.
(b) The statement is false because Tallahassee is the capital of Florida, so it is not a proposition. Its truth value is false.
(c) The statement is true, so it is a proposition. Its truth value is True.
(d) The statement is false because 5 + 7 = 12, so it is not a proposition. Its truth value is false.
(e) The statement is true when x = 9 and it is false when x is not equal 9. Therefore, the statement is a proposition when x = 9 and it is not a proposition when x is not equal 9. Its truth value could be true or false.
(f) The statement is correct, so it is true. It is a proposition and its truth value is true.

After checking my answers. (b), (d), (e) and (f) marked as wrong. I was so shocked. I followed the logic of a proposition and I have no idea what I am missing?

 

[khansaheb]

Which of these sentences are propositions? What are the truth values of those that are propositions?

(a) Boston is the capital of Massachusetts.
(b) Miami is the capital of Florida.
(c) 2 + 3 = 5.
(d) 5 + 7 = 10.
(e) x + 2 = 11.
(f) Answer this questions.


My attempt.

A proposition is a statement that is true.

(a) The statement is true, so it is a proposition. Its truth value is True.
(b) The statement is false because Tallahassee is the capital of Florida, so it is not a proposition. Its truth value is false.
(c) The statement is true, so it is a proposition. Its truth value is True.
(d) The statement is false because 5 + 7 = 12, so it is not a proposition. Its truth value is false.
(e) The statement is true when x = 9 and it is false when x is not equal 9. Therefore, the statement is a proposition when x = 9 and it is not a proposition when x is not equal 9. Its truth value could be true or false.
(f) The statement is correct, so it is true. It is a proposition and its truth value is true.

After checking my answers. (b), (d), (e) and (f) marked as wrong. I was so shocked. I followed the logic of a proposition and I have no idea what I am missing?

In mathematics, we are interested in statements that can be proved or disproved. We define

a proposition (sometimes called a statement, or an assertion) to be a sentence that is either true or false, but not both.​

​

Propositions do not have to be true.

So (b) is a "false" proposition - a proposition nonetheless.

and so on.....

 

[Dr.Peterson]

Which of these sentences are propositions? What are the truth values of those that are propositions?

(a) Boston is the capital of Massachusetts.
(b) Miami is the capital of Florida.
(c) 2 + 3 = 5.
(d) 5 + 7 = 10.
(e) x + 2 = 11.
(f) Answer this questions.


My attempt.

A proposition is a statement that is true.

(a) The statement is true, so it is a proposition. Its truth value is True.
(b) The statement is false because Tallahassee is the capital of Florida, so it is not a proposition. Its truth value is false.
(c) The statement is true, so it is a proposition. Its truth value is True.
(d) The statement is false because 5 + 7 = 12, so it is not a proposition. Its truth value is false.
(e) The statement is true when x = 9 and it is false when x is not equal 9. Therefore, the statement is a proposition when x = 9 and it is not a proposition when x is not equal 9. Its truth value could be true or false.
(f) The statement is correct, so it is true. It is a proposition and its truth value is true.

After checking my answers. (b), (d), (e) and (f) marked as wrong. I was so shocked. I followed the logic of a proposition and I have no idea what I am missing?

Did you look up a definition??

Wikipedia won't be helpful; but here is a randomly chosen textbook definition:

A proposition is a sentence to which one and only one of the terms true or false can be meaningfully applied.​

Here is another discussion, which touches on an important detail.

A proposition does not have to be true! (Why do you think they asked separately for the truth value?)

Give it another try. (I suggest reading what the book says.)

 

[mario99]

In mathematics, we are interested in statements that can be proved or disproved. We define

a proposition (sometimes called a statement, or an assertion) to be a sentence that is either true or false, but not both.​

​

Propositions do not have to be true.

So (b) is a "false" proposition - a proposition nonetheless.

and so on.....

Thank you khansaheb


Ohh, false is also a proposition. First time to know. Knowledge increased.

Did you look up a definition??

Wikipedia won't be helpful; but here is a randomly chosen textbook definition:

A proposition is a sentence to which one and only one of the terms true or false can be meaningfully applied.​

Here is another discussion, which touches on an important detail.

A proposition does not have to be true! (Why do you think they asked separately for the truth value?)

Give it another try. (I suggest reading what the book says.)

Thank you Dr.Peterson


I will not say the definition of Wiki is not helpful.
A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity.

At the end it mentioned the main idea: the primary bearer of truth or falsity. I will just pretend that this means a proposition is a true or a false statement, not both, as khansaheb said.

The second definition:
Sentences considered in propositional logic are not arbitrary sentences but are the ones that are either true or false, but not both. This kind of sentences are called propositions. I think that this is the easiest to understand.

The third definition:
A proposition is a sentence to which one and only one of the terms true or false can be meaningfully applied.

When I read the third definition, everything is good until......can be meaningfully applied. I don't understand this part. Does it intend to say here that when the statement doesn't make sense which means it is meaningless, we conclude that it is in fact not a statement. In other words, it doesn't deserve to be a proposition.

After reading the three definitions, I grasped some knowledge. I understand why they asked separately for the truth value. I also understand why (b) and (d) were wrong. But I don't understand why (e) and (f) were wrong.

 

[Dr.Peterson]

I also understand why (b) and (d) were wrong. But I don't understand why (e) and (f) were wrong.

(a) Boston is the capital of Massachusetts.
(b) Miami is the capital of Florida.
(c) 2 + 3 = 5.
(d) 5 + 7 = 10.
(e) x + 2 = 11.
(f) Answer this questions.

(a) The statement is true, so it is a proposition. Its truth value is True.
(b) The statement is false because Tallahassee is the capital of Florida, so it is not a proposition. Its truth value is false.
(c) The statement is true, so it is a proposition. Its truth value is True.
(d) The statement is false because 5 + 7 = 12, so it is not a proposition. Its truth value is false.
(e) The statement is true when x = 9 and it is false when x is not equal 9. Therefore, the statement is a proposition when x = 9 and it is not a proposition when x is not equal 9. Its truth value could be true or false.
(f) The statement is correct, so it is true. It is a proposition and its truth value is true.

(e) Can you tell whether it is true or false, without knowing the value of x?

This is the reason I didn't stop with the definition I quoted, but gave the last reference "which touches on an important detail". Here is that detail, which I expected you to read:

Also "x is greater than 2", where x is a variable representing a number, is not a proposition,
because unless a specific value is given to x we can not say whether it is true or false, nor do we know what x represents.

(f) This, too, is covered explicitly in that last link, though the quoted definition is sufficient:

But "Close the door", and "Is it hot outside ?"are not propositions.

These are not statements in the first place; they are a command and a question.

What is its truth value? If it can't be determined, then it isn't a proposition.

 

[khansaheb]

which I expected you to read:

Reading and pontificating is painful......

 

[mario99]

(e) Can you tell whether it is true or false, without knowing the value of x?

No, I cannot and this is the reason it is not a proposition. hmm This is very interesting.

(e) Can you tell whether it is true or false, without knowing the value of x?

This is the reason I didn't stop with the definition I quoted, but gave the last reference "which touches on an important detail". Here is that detail, which I expected you to read:

(f) This, too, is covered explicitly in that last link, though the quoted definition is sufficient:

These are not statements in the first place; they are a command and a question.

What is its truth value? If it can't be determined, then it isn't a proposition.

You are awesome Dr.Peterson. I think that I have fully understood my mistakes.

I have just to pay more attention in the future to differentiate between commands, questions, and statements.

In conclusion, we don't care if it is a true or false statement, we just need to know if it is true or false to say that it is a proposition.