For each of the following compound statement first identify the connecting words and then break it into component statements.

(i) All rational numbers are real and all real numbers are not complex.

(ii) Square of an integer is positive or negative.

(iii) The sand heats up quickly in the sun and does not cool down fast at night.

(iv) x = 2 and x = 3 are the roots of the equation $3 x^{2} - x - 10 = 0$ .

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Solution

(i) The component statement has the connecting word 'and' component statements are

p : All rational numbers are real.

q : All real numbers are not complex.

(ii) The component statement has the connecting words 'or' component statements

p : Square of an integer is positive.

q : Square of an integer is negative.

(iii) The component statement has the connecting word 'and' component statements are

p : The sand heats up quickly in the sun.

q : The sand does not cool down fast at night.

(iv) The component statement has the connecting word 'and' component statements are

p : x = 2 is a root of the equation $3 x^{2} - x - 10 = 0.$

q : x = 3 is a root of the equation $3 x^{2} - x - 10 = 0.$

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Similar questions

x = 2

x = 3

3 x^{2} - x - 10 = 0

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 $3 x^{2} - x - 10 = 0.$

(a - b + c) x^{2} + 2 (a - b) x + (a - b - c) = 0

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