Q6 of 18 Page 13

For each of the following compound statements 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 3x2 – x – 10 = 0.


(i) "AND"
The component statements are:
All rational numbers are real.
All rational numbers are complex.

(ii) "OR"
The component statements are:
Square of an integer is positive.
Square of an integer is negative.

(iii) "AND"
The component statements are:
The sand heats up quickly in the sun.
The sand does not cool down fast at night.

(iv) "AND"
The component statements are:
x = 2 is a root of the equation 3x2 – x – 10 = 0
x = 3 is a root of the equation 3x2 – x – 10 = 0

More from this chapter

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4
Are the following pairs of statements negations of each other:

(a) The number x is not a rational number. The number x is not an irrational number.

(b) The number x is a rational number. The number x is an irrational number.

5
Find the component statements of the following compound statements and check whether they are true or false.

(i) The sun shines or it rains.

(ii) All integers are positive or negative.

(iii) 100 is divisible by 3, 11 and 5.

7
Identify the quantifier in the following statements and write the negation of the statements.

(i) There exists a number which is equal to its square.

(ii) For every real number x, x is less then x + 1.

(iii) There exists a capital for every state in India.

8
Check whether the following pair of statements is negation of each other. Give reasons for your answer.

(i) x + y = y + x is true for every real number x and y.

(ii) There exists a real number x and y for which x + y = y + x.