Which of the following sentences are statements? Give reasons for your answer.
All real numbers are complex numbers.
All real numbers are complex numbers.
(A) complex number is defined as a number of the form $a + bi$,where $a$ and $b$ are real numbers and $i = \sqrt{-1}$.
Any real number $x$ can be expressed as $x + 0i$.
Since every real number can be written in the form $a + bi$,the sentence 'All real numbers are complex numbers' is always true.
Therefore,it is a statement.
Any real number $x$ can be expressed as $x + 0i$.
Since every real number can be written in the form $a + bi$,the sentence 'All real numbers are complex numbers' is always true.
Therefore,it is a statement.
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Similar Questions
If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...
Which one of the following is the pair of equivalent circuits?
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$
$i. (p \land q) \lor (p \land r)$
$ii. p \lor (q \land r)$
$iii. p \land (q \lor r)$
$iv. p \land q \land r$
$v. (p \land q) \lor r$
If $(p \wedge \sim r) \rightarrow (\sim p \vee q)$ has a truth value of $False$,then the truth values of $p, q, r$ are respectively:
Statement $-1 :$ $\sim (p \leftrightarrow \sim q)$ is equivalent to $p \leftrightarrow q$.
Statement $-2 :$ $\sim (p \leftrightarrow \sim q)$ is a tautology.
Statement $-2 :$ $\sim (p \leftrightarrow \sim q)$ is a tautology.
DifficultAIEEE 2009
View SolutionStatement-$I$: $\sim (p \leftrightarrow q)$ is equivalent to $(p \wedge \sim q) \vee (q \wedge \sim p)$.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.
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