# Need help in logic and statements

I am stuck with some questions. Please help me out. Thanks.

If $P(x):x^2 < 12$, then $P(1.5)$ is a statement (I think yes. As the Universe of $x$ is not given but can be taken as set of Real Numbers.)

If $Q(n): n+3=6$, then $Q(m)$ is the statement (I think no. As $m$ is a variable and we can not have variables or undetermined values in a statement.)

If $P(y): 1+2+3+\ldots+y =0$, then $P(5)$ is the statement (I think yes.)

If $Q(m):m \leq 3^m$, then $Q(k)$ is the statement. (I think no. As $m$ is a variable and we can not have variables or undetermined values in a statement.)

Where Statement is a sentence that evaluates to either true or false but not both.

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By "statement", do you mean a well-formed formula with no free variables? (sometimes called a "sentence"). – Arturo Magidin Sep 28 '11 at 18:14
Are you sure? In the third edition they define a statement to be a declarative sentence that is either true or false but not both. – Brian M. Scott Sep 28 '11 at 18:37
@Arturo: Akito almost certainly won’t know the terms well-formed formula and free variable, and unless the sixth edition of KB&R is astonishingly different from the third, the technical meaning of sentence in logic will also be unfamiliar. – Brian M. Scott Sep 28 '11 at 18:39
If Brian's definition is the correct one, then your thinking seems to be correct in all four items. – Arturo Magidin Sep 28 '11 at 18:40
Then I agree with Arturo: you’ve answered all four of them correctly and given appropriate reasons. – Brian M. Scott Sep 28 '11 at 18:58

## 1 Answer

A CW post to eliminate this question from the Unanswered queue.

As has been remarked in the comments, your suggested answers and accompanying reasoning, which yield the answers:

Yes, No, Yes, No

are all correct. Cheers!

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