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.

Explanation

(i) p: A line is straight.
q: A line extends indefinitely in both the directions.
(p and q) is true.
(ii) p: A point occupies a position.
q: The location of a point can be determined.
(p and q) is true.
(iii) p: The sand heats up quickly in the sun.
q: The hot sand does not cool down fast at night.
(p and q) is true.
(iv) p: 32 is divisible by 8.
q: 32 is divisible by 12.
(p and q) is not true.
(v) p: x = 1 is a root of the equation `x^(2) -x -2 = 0.`
q: x = 2 is a root of the equation `x^(2) -x-2 = 0.`
(p and q) is not true.
(vi) p: 3 is rational.
`q: sqrt(3)` is irrational.
(p and q) is true.
(vii) p: All integers are rational numbers.
q: All rational numbers are not real numbers.
(p and q) is false.
(viii) p: Lucknow is in Uttar Pradesh.
q: Kanpur is in Uttarakhand.
(p and q) is false.