Check whether the following sentence is a statement. Give reasons for your answer.
"Every set is a finite set."
"Every set is a finite set."
(N/A) sentence is considered a statement in logic if it is either true or false,but not both.
The sentence "Every set is a finite set" is a declarative sentence.
Since there exist infinite sets (e.g.,the set of all natural numbers $\mathbb{N}$),the statement "Every set is a finite set" is false.
Because the sentence has a definite truth value (it is false),it is a statement.
The sentence "Every set is a finite set" is a declarative sentence.
Since there exist infinite sets (e.g.,the set of all natural numbers $\mathbb{N}$),the statement "Every set is a finite set" is false.
Because the sentence has a definite truth value (it is false),it is a statement.
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Similar Questions
The entries in the last column of the truth table for $\sim(p \wedge q)$ are
Which of the following statement$(s)$ is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.
The negation of the compound proposition $p \vee (\sim p \vee q)$ is
Easy
View SolutionWhich of the following statement patterns is a tautology?
Which one of the following is the pair of equivalent circuits?
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$
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