Check whether the following sentence is a statement. Give reasons for your answer.
Mathematics is fun.
Mathematics is fun.
(N/A) sentence is considered a statement in logic if it is either true or false,but not both.
This sentence is subjective because for some people,mathematics is fun,while for others,it may not be.
Since the truth value of this sentence depends on the individual's opinion,it is not always true or always false.
Therefore,it is not a statement.
This sentence is subjective because for some people,mathematics is fun,while for others,it may not be.
Since the truth value of this sentence depends on the individual's opinion,it is not always true or always false.
Therefore,it is not a statement.
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If $S^*(p, q, r)$ is the dual of the compound statement $S(p, q, r)$ and $S(p, q, r) = \sim p \wedge [\sim (q \vee r)]$,then $S^*(\sim p, \sim q, \sim r)$ is equivalent to:
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View SolutionThe negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:
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.
Let $a : \sim (p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false,then the truth values of $a$ and $b$ are respectively:
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