AP Board Class 9 Maths Chapter 15 Proofs in Mathematics Ex 15.1 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 Book Answers ~ HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 9 Maths Chapter 15 Proofs in Mathematics Ex 15.1 Textbook Solutions PDF: Download Andhra Pradesh Board STD 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 Book Answers

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Andhra Pradesh State Board Class 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 Books Solutions

Board	AP Board
Materials	Textbook Solutions/Guide
Format	DOC/PDF
Class	9th
Subject	Maths
Chapters	Maths Chapter 15 Proofs in Mathematics Ex 15.1
Provider	Hsslive

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AP State Syllabus 9th Class Maths Solutions 15th Lesson Proofs in Mathematics Exercise 15.1

Question 1.
State whether the following sentences are always true, always false or ambiguous. Justify your answer.
i) There are 27 days in a month.
Solution:
Always false. Generally 30 days or 31 days make a month except February.

ii) Makarasankranthi fells on a Friday.
Solution:
Ambiguous. Makarasankranthi may fall on any day of the week.

iii) The temperature in Hyderabad is 2°C.
Solution:
Ambiguous. Sometimes the temperature may go down to 2°C in winter.

iv) The earth is the only planet where life exist.
Solution:
We can’t say always true. To the known fact, so far we can say this.

v) Dogs can fly.
Solution:
Always false,’as dogs can never fly.

vi) February has only 28 days.
Solution:
Ambiguous. A leap year has 29 days for February.

Question 2.
State whether the following statements are true or false. Give reasons for your answers.

i) The sum of the interior angles of a quadrilateral is 350°.
Solution:
False. Sum of the interior angles of a quadrilateral is 360°.

ii) For any real number x, x² > 0
Solution:
True. This is true for all real numbers,

iii) A rhombus is a parallelogram.
Solution:
True. In a rhombus, both pairs of opposite sides are parallel and hence every rhombus is a parallelogram.

iv) The spm of two even numbers is even.
Solution:
True. This is true for any two even numbers.

v) Square numbers can be written as the sum of two odd numbers.
Solution:
Ambiguous. Since square of an odd number can’t be written as sum of two odd numbers.

Question 3.
Restate the following statements with appropriate conditions, so that they become true statements.

i) All numbers can be represented in prime factorization.
Solution:
Any natural number greater than 1 can be represented in prime factorization.

ii) Two times a real number is always even.
Solution:
Two times a natural number is always even.

iii) For any x, 3x + 1 > 4.
Solution:
For any x > 1; 3x + 1 > 4.

iv) For any x, x³ ≥ 0.
Solution:
For any x > 0; x³ ≥ 0.

v) In every triangle, a median is also an angle bisector.
Solution:
In an equilateral triangle, a median is also an angle bisector.

Question 4.
Disprove, by finding a suitable counter example, the statement
x² > y² for all x > y.
Solution:
If x = – 8 and y = – 10
Here x > y
x² = (- 8)² = 64 and y² = (- 10)² = 100
But x² > y² is false here. [ ∵ 64 < 100]
(This can be proved for any set of nega-tive numbers or a negative number and a positive number)

AP Board Textbook Solutions PDF for Class 9th Telugu

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Andhra Pradesh Board Class 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 exam preparation. The AP Board STD 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 9th Maths Chapter 15 Proofs in Mathematics Ex 15.1 Books State Board syllabus with maximum efficiency.

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