Discrete Mathematics (Statement)

Question

1) x^2 + x + 1 = 0 , x is a real number.

Answer: Is a statement.

2) x^2 + x + 1 = 0 , x is complex number.

Answer: Is not a statement.

Why the question no.2 is not a statment ?

I'm voting to close this question as off-topic because it is about [math.se] instead of programming or software development. — Pang, Jan 25 '18 at 02:41

score 0 · Answer 1 · answered Jan 23 '18 at 07:33

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Reason: A Statement is a declarative statement that is either true or false but not both.

answered Jan 23 '18 at 07:33

Sivaram Boina

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But not both. Then the answer for question no.1 should also be not a statement. Am I right ? – Jiale Jan 23 '18 at 07:41
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That can be considered as a statement because it is always false regardless of how x is chosen. This is because there is no real number which satisfies this equation. Therefore, it is guaranteed to have a definite truth value: false. – Sivaram Boina Jan 25 '18 at 08:33

score 0 · Accepted Answer · answered Jan 23 '18 at 18:51

To expand on Jiale's answer:

A statement is a statement which has a definite truth value.

1) x^2 + x + 1 = 0 , x is a real number.

This can be considered a statement because it is always false regardless of how x is chosen. This is because there is no real number which satisfies this equation. Therefore, it is guaranteed to have a definite truth value: false.

2) x^2 + x + 1 = 0 , x is complex number.

This cannot be considered a statement because it is true for some complex numbers x, and false for others. The truth value of this expression is only definite once x is specified. Therefore, it is not a statement.

Discrete Mathematics (Statement)

2 Answers2