For each of the following compound statements first identify the connecting words and then break it into component statements.

Question:

For each of the following compound statements first identify the connecting words and then break it into component statements.

(i) All rational numbers are real and all real numbers are not complex.

(ii) Square of an integer is positive or negative.

(iii) The sand heats up quickly in the Sun and does not cool down fast at night.

(iv) $x=2$ and $x=3$ are the roots of the equation $3 x^{2}-x-10=0$.

Solution:

(i) Here, the connecting word is ‘and’.

The component statements are as follows.

p: All rational numbers are real.

q: All real numbers are not complex.

(ii) Here, the connecting word is ‘or’.

The component statements are as follows.

p: Square of an integer is positive.

q: Square of an integer is negative.

(iii) Here, the connecting word is ‘and’.

The component statements are as follows.

p: The sand heats up quickly in the sun.

q: The sand does not cool down fast at night.

(iv) Here, the connecting word is ‘and’.

The component statements are as follows.

$p: x=2$ is a root of the equation $3 x^{2}-x-10=0$

$q: x=3$ is a root of the equation $3 x^{2}-x-10=0$