Split each of the following into simple sentences and determine

Solution:

(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