Question

Split each of the following compound statement 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 $3x^2-x-10=0.$

Answer 1

(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 statment is false.

(iii) Let p: All rational numbers are real.

And, q: All real numbers are not complex numbers.

Clearly, p is true and q is false.

$\therefore$ (p and q) is false.

Hence, p is true and q 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, $3\times 5^2-5=10=60\ne 0.$ So, $x=5$ is not a root of the equation $3x^2-x-10=0.$

And, $3\times 2^2-2-10=0.$ 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.