Question

Consider the. following compound statement
(i) Mumbai is the capital of Rajasthan or Maharashtra,
(ii) $\sqrt{3}$ is a rational number or an irrational number,
(iii) $125$ is a multiple of $7$ or $8$
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true?

• A. (i)
• B. (ii)
• C. (iii)
• D. (Iv)

Answer 1

Answer: (C)

(iii)

(i) The component statements of " Mumbai is the capital of Rajasthan or Maharashtra" are
$p:$ Mumbai is the capital of Rajasthan.
$q:$ Mumbai is the capital of Maharashtra.
We note that $p$ is false and $q$ is true, so the compound statement is true
(ii) The component statements of $\sqrt{3}$ is a rational or an irrational are
$p:$ $\sqrt{3}$ is a rational number.
$q:$ $\sqrt{3}$ is an irrational number.
We note that $p$ is false and $q$ is true, so the compound statement is true.
(iii) The component statements of $125$ is a multiple of $7$ or $8$ are
$p:125$ is a multiple of $7.$
$q:125$ is a multiple of $8.$
We note that $p$ and $q$ both are false statements, so compound statement is false.
(iv) The component statements of "A rectangle is a quadrilateral or a regular hexagon." are
$p:A$ rectangle is a quadrilateral.
$q:A$ rectangle is a regular hexagon.
We note that $p$ is true and $q$ is false, so the compound statement is true.