The Student Room Group

Help in Math: What is Statement?

I'm preparing TMUA and reading the material about TMUA provided by authority. But there are several confusing points.
(1)Is 'positive integer x is divisible by 2' a statement?
(2)Is 'if x is a positive integer, x is divisible by 2' a statement?
(3)Is 'if positive integer x is divisible by 3, x is divisible by 2" a statement?
What is statement? A sentence that is either true or false but not both? If so, (1) (2) (3) cannot be statements since there are some values of x that make the sentence true but others make the sentence false.
Reply 1
Original post by ECFDPB
I'm preparing TMUA and reading the material about TMUA provided by authority. But there are several confusing points.
(1)Is 'positive integer x is divisible by 2' a statement?
(2)Is 'if x is a positive integer, x is divisible by 2' a statement?
(3)Is 'if positive integer x is divisible by 3, x is divisible by 2" a statement?
What is statement? A sentence that is either true or false but not both? If so, (1) (2) (3) cannot be statements since there are some values of x that make the sentence true but others make the sentence false.

Do you have the question or context (notes) of where these statements come from?
Reply 2
Original post by mqb2766
Do you have the question or context (notes) of where these statements come from?

I make up (2) (3), but on the note, (1) is considered as 'not a sentence'
Here's the note https://uat-wp.s3.eu-west-2.amazonaws.com/wp-content/uploads/2024/05/16150136/Notes_on_Logic_and_Proof_May2024.pdf
You can see (1) at the end of page 7
Reply 3
Original post by mqb2766
Do you have the question or context (notes) of where these statements come from?
I wrote an email to authority but the authority didn't respond to me
1111.png
Reply 4
Original post by ECFDPB
I make up (2) (3), but on the note, (1) is considered as 'not a sentence'
Here's the note https://uat-wp.s3.eu-west-2.amazonaws.com/wp-content/uploads/2024/05/16150136/Notes_on_Logic_and_Proof_May2024.pdf
You can see (1) at the end of page 7

For (1) thats pretty much covered in the notes, so preceding sentence and first paragraph of page 8.
Reply 5
Original post by ECFDPB
I wrote an email to authority but the authority didn't respond to me
1111.png

For the red statement, it would be false as a^2<b^2 does not always imply 0<a<b.
Reply 6
Original post by mqb2766
For (1) thats pretty much covered in the notes, so preceding sentence and first paragraph of page 8.

I know! I mean, according to notes, it seems like that anything in the form of 'if A then B' is a statement. But if so, what's the difference between (1) and (2)? Why (1) is not a statement but (2) is a statement?
Reply 7
Original post by ECFDPB
I know! I mean, according to notes, it seems like that anything in the form of 'if A then B' is a statement. But if so, what's the difference between (1) and (2)? Why (1) is not a statement but (2) is a statement?

On page 24 of the notes they discuss statements of the form IF A THEN B, and (1) is covered in the notes on page 8. Loosely, if all elements of A are also in B, then the statement IF A THEN B is true, otherwise its false. So you just need one counter example to negate it. For (1), as in the notes and as you note above, its an expression.
Reply 8
Original post by mqb2766
On page 24 of the notes they discuss statements of the form IF A THEN B, and (1) is covered in the notes on page 8. Loosely, if all elements of A are also in B, then the statement IF A THEN B is true, otherwise its false. So you just need one counter example to negate it. For (1), as in the notes and as you note above, its an expression.

Can I consider all expression in the form of ' if A then B ' as a statement?🤔 Vert strange I have to say
Reply 9
Original post by ECFDPB
Can I consider all expression in the form of ' if A then B ' as a statement?🤔 Vert strange I have to say

Assuming A and B are suitably defined, then yes. You can check whether all elements of A are in B.

As they say in the notes, (1) is really talking about a single element which is a positive integer so to say whether its divisible by 2 or not, you need to know what value it is. In (2), A is the set of all positive integers and the simple counter example, 1 is in A but not B (divisible by 2), means its false.

Quick Reply