Write the contrapositive and converse of the following statement:
'Something is cold implies that it has low temperature.'
'Something is cold implies that it has low temperature.'
(N/A) Let $p$ be the statement 'Something is cold' and $q$ be the statement 'It has low temperature'.
The given statement is of the form $p \implies q$.
The contrapositive of $p \implies q$ is $\neg q \implies \neg p$.
Thus,the contrapositive is: 'If something does not have low temperature,then it is not cold.'
The converse of $p \implies q$ is $q \implies p$.
Thus,the converse is: 'If something has low temperature,then it is cold.'
The given statement is of the form $p \implies q$.
The contrapositive of $p \implies q$ is $\neg q \implies \neg p$.
Thus,the contrapositive is: 'If something does not have low temperature,then it is not cold.'
The converse of $p \implies q$ is $q \implies p$.
Thus,the converse is: 'If something has low temperature,then it is cold.'
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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.
Which of the following statements is a tautology?
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$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.
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$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.
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