Page No 324:
Question 1:
Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.

Page No 329:
Question 1:
Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu.
(ii) is not a complex number.
(iii) All triangles are not equilateral triangle.
(iv) The number 2 is greater than 7.
(v) Every natural number is an integer.

Page No 329:
Question 2:
Are the following pairs of statements negations of each other?
(i) The number x is not a rational number.
The number x is not an irrational number.
(ii) The number x is a rational number.
The number x is an irrational number.

Page No 342:
Question 1:
Show that the statement
p: “If x is a real number such that x³ + 4x = 0, then x is 0” is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive

Page No 342:
Question 1:
Show that the statement
p: “If x is a real number such that x³ + 4x = 0, then x is 0” is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive

Page No 342:
Question 3:
Show that the following statement is true by the method of contrapositive.
p: If x is an integer and x² is even, then x is also even.

Page No 342:
Question 4:
By giving a counter example, show that the following statements are not true.
(i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
(ii) q: The equation x² – 1 = 0 does not have a root lying between 0 and 2.

Page No 343:
Question 5:
Which of the following statements are true and which are false? In each case give a valid reason for saying so.
(i) p: Each radius of a circle is a chord of the circle.
(ii) q: The centre of a circle bisects each chord of the circle.
(iii) r: Circle is a particular case of an ellipse.
(iv) s: If x and y are integers such that x > y, then –x < –y.
(v) t: is a rational number.

Page No 345:
Question 1:
Write the negation of the following statements:
(i) p: For every positive real number x, the number x – 1 is also positive.
(ii) q: All cats scratch.
(iii) r: For every real number x, either x > 1 or x < 1.
(iv) s: There exists a number x such that 0 < x < 1.

Page No 345:
Question 2:
State the converse and contrapositive of each of the following statements:
(i) p: A positive integer is prime only if it has no divisors other than 1 and itself.
(ii) q: I go to a beach whenever it is a sunny day.
(iii) r: If it is hot outside, then you feel thirsty.

Page No 345:
Question 3:
Write each of the statements in the form “if p, then q”.
(i) p: It is necessary to have a password to log on to the server.
(ii) q: There is traffic jam whenever it rains.
(iii) r: You can access the website only if you pay a subscription fee.

Page No 345:
Question 4:
Re write each of the following statements in the form “p if and only if q”.
(i) p: If you watch television, then your mind is free and if your mind is free, then you watch television.
(ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.
(iii) r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Page No 345:
Question 5:
Given below are two statements
p: 25 is a multiple of 5.
q: 25 is a multiple of 8.
Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.

Page No 345:
Question 6:
Check the validity of the statements given below by the method given against it.
(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).
(ii) q: If n is a real number with n > 3, then n² > 9 (by contradiction method).

Page No 345:
Question 7:
Write the following statement in five different ways, conveying the same meaning.
p: If triangle is equiangular, then it is an obtuse angled triangle.