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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The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...
Which of the following is not a tautology?
Medium
View SolutionStatement $-1 :$ $\sim (p \leftrightarrow \sim q)$ 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 SolutionLet $p$ be the statement '$x$ is an irrational number',$q$ be the statement '$y$ is a transcendental number',and $r$ be the statement '$x$ is a rational number or $y$ is a transcendental number'.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.
Statement-$1$: $r$ is equivalent to $q \lor p$.
Statement-$2$: $r$ is equivalent to $(p \Leftrightarrow \sim q)$.
Medium
View SolutionNegation of the statement $(p \vee r) \Rightarrow (q \vee r)$ is :
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