Split each of the following compound statements into simple sentences and determine whether it is true or false: (i) The grass is green and the sky is blue. (ii) Agra is in Uttar Pradesh and Shimla is in Punjab. (iii) All rational numbers are real and all real numbers are not complex numbers. (iv) x = 5 and x = 2 are the roots of the equation `3x^(2)-x-10=0`

Explanation

(i) Let p: The grass is green.
And q: The sky is blue.
Clearly, each one of p and q is a true statement and therefore, (p and q) is true.
Hence, the given statement is true.
(ii) Let p: Agra is in Uttar Pradesh.
And q: Shimla is in Punjab.
Clearly, p is true and q is false.
Therefore, (p and q) is false.
Hence, the given statement is false.
(iii) Let p: All rational numbers are real.
And, q: All real number are not complex numbers.
Clearly, p is true and q is false.
`therefore" "` (p and q) is false.
Hence, the given statement is false.
(iv) Let p: x=5 is a root of the equation `3x^(2)-x-10=0`
And q: x=2 is a root of the equation `3x^(2)-x-10=0`
Clearly, `3xx5^(2)-5-10=60 ne 0.` So, x=5 is not a root of the
equation `3x^(2)-x-10=0.`
And, `3xx2^(2)-2-10=0.` So, x=2 is a root of `3x^(2)-x-10=0`
`therefore` p is false and q is true.
Consequently, (p and q) is false.
Hence, the given statement is false.