Split each of the following into simple sentences and determine whether it is true or false.
(i) A line is straight and extends indefinitely in both the directions.
(ii) A point occupies a position, and its location can be determined.
(iii) The sand heats up quickly in the sun and does not cool down fast at night. (iv) 32 is divisible by 8 and 12 .
(v) $x=1$ and $x=2$ are the roots of the equation $x^{2}-x-2=0$.
(vi) 3 is rational, and $\sqrt{3}$ is irrational.
(vii) All integers are rational numbers, and all rational numbers are not real numbers.
(viii) Lucknow is in Uttar Pradesh, and Kanpur is in Uttarakhand.
(i) p: A line is straight.
q: A line extends indefinitely in both the directions.
Both the simple sentences are TRUE; therefore, the given sentence is TRUE.
(ii) p: A point occupies a position.
q: Its location can be determined.
Both the simple sentences are TRUE; therefore, the given sentence is TRUE.
(iii) p: The sand heats up quickly in the sun.
q: The sand does not cool down fast at night.
The first sentence is TRUE and the second sentence is FALSE.
Therefore the given sentence is FALSE.
(iv) p: 32 is divisible by $8 .$
q: 32 is divisible by 12 .
First sentence is TRUE. Second sentence is FALSE.
Therefore the given sentence is FALSE.
(v) $p: x=1$ is a root of the equation $x^{2}-x-2=0$
$\mathrm{q}: \mathrm{x}=2$ is a root of the equation $\mathrm{x}^{2}-\mathrm{x}-2=0$
So, the first sentence is FALSE. Second sentence is TRUE.
Therefore, the given sentence is FALSE.
(vi) p: 3 is rational.
q: $\sqrt{3}$ is irrational.
First sentence is TRUE. Second sentence is TRUE.
Both the sentences are TRUE; therefore the given sentence is TRUE.
(vii) p: All integers are rational numbers.
q: All rational numbers are not real numbers.
First sentence is TRUE. Second sentence is FALSE.
Therefore, the given sentence is FALSE.
(viii) p: Lucknow is in Uttar Pradesh.
q: Kanpur is in Uttarakhand.
First sentence is TRUE. Second sentence is FALSE.
Therefore, the given sentence is FALSE