AP State Syllabus AP Board 9th Class Maths Solutions Chapter 15 Proofs in Mathematics InText Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 15th Lesson Proofs in Mathematics InText Questions

**Do This**

Question

Make 5 more sentences and check whether they are statements or not ? * Give reasons. [Page No. 311]

Solution:

1) 9 is a prime number – False

This is a statement because we can judge the truthness of this sentence. Clearly it is a false statement as 9 has factors other than 1 and 9, hence it is a composite number.

2) x is less than 5 – can’t say True or False

This is not a statement. The truthness can t be verified unless the value of x is known. Hence it is a sentence only.

3) 3 + 5 = 8 – True

The above sentence is a statement. It is a true statement as 5 + 3 = 8.

4) Sum of two odd numbers is even – True

The above sentence can be verified as a true sentence by taking ex¬amples like 3 + 5 = 8, 5 + 7 = 12 etc. Hence it is a true statement.

5) \(\frac{\mathrm{X}}{2}\) +3 = 9- can’t say True or False.

The above sentence is not a state¬ment. Its truthness can’t be

verified without the value of x.

**Try This**

1. 3 is a prime number.

2. Product of two odd integers is even.

3. For any real number x; 4x T x = 5x

4. The earth has one moon.

5. Ramu is a good driver.

6. Bhaskara has written a book “Leelavathi ”.

7. All even numbers are composite.

8. A rhombus is a square.

9. x > 7.

10. 4 and 5 are relative primes.

11. Silver fish is made of silver.

12. Humans are meant to rule the earth.

13. For any real number .v. 2x > x.

14. Havana is the capital of Cuba.

Question

Which of the above statements can be tested by giving counter example ?

[Page No. 312]

Solution:

Statements 2, 7, 8, 13 can be tested by giving counter examples 2) Product of two odd integers is even. Counter example.

2) Product of two odd integers 3 and 5 is 3×5 = 15 is not an even number.

7) All even numbers are composite. Counter example : 2 is an even prime.

8) A rhombus is a square.

Counter example: (40°, 140°, 40°. 140°) is a rhombus.

13) For anyx; 2x > x

Counter example : for x = -3:

2x = 2(-3) = – 6

here -6 < – 3

b

**Try This**

Envied by the popularity of Pythagoras, his younger brother claimed a different relation between the sides of a right angled triangles. [Page No. 319]

Liethagoras Theorem: In any right angled triangle the square of the smallest side equals the sum of the other sides. Check this conjecture, whether It is right or wrong.

Solution:

This conjecture is true for the above

triangles.

i) 3^{2} 5 + 4 ⇒ 9 = 5 + 4

ii) 52 = 25 = 12 + 13

iii) 7^{2} = 49 = 24 + 25

But, when the smallest side happens to be an even integer the conectiire may not hods good.

Eg: 1) 6^{2 }= 36 ≠ 10 + 8

ii) 12^{2} = 144 ≠ 20 + 16