PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Give three examples of sentences which are not statements. Give reasons for the answers.

Write the negation of the statement:
Banglore is the capital of Karnataka.

Write the negation of the statement:

 It rained on July 4, 2005.

Write the negation of the statement:

 Ravish is honest.

Write the negation of the statement:

 The earth is round.

Write the negation of the statement:

All birds sing.

 Some even integers are prime.

There is a complex number which is not a real number.

 I will not go to school.

 Both the diagonals of a rectangle have the same length.

Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.

Are the pair of statement are negation of each other:

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

Write the negation of the statement:

 p : For every positive real number x, the number (x − 1) is also positive.

Write the negation of the statement:

q : For every real number x, either x > 1 or x < 1.

Write the negation of the statement:

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
 There exist real numbers a and b for which a + b = b + a.

Find the component statement of the compound statement:
 The sky is blue and the grass is green.

Find the component statement of the compound statement:

The earth is round or the sun is cold.