Home
Class 12
MATHS
By giving counter example show that foll...

By giving counter example show that following statement are false
(a) p : Square of a real number is always integer
(b) p : The equation `x^2-9=0` does not have a root lying between 0 and 4

Text Solution

Verified by Experts

(a) Let a real number x=1.5
so, `x^2=2.25`, which is not an integer
So, p is false
(b) Given equation is `x^2-9=0`
Now, putting x=3 in `x^2-9`
`(3)^2-9`
`rArr 9-9`
`rArr 0`
So, 3 is a root of equation and lies between 0 and 4
So, p is false
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-A) (Objective type Questions (Only one answer))|50 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-B) (Objective type Questions (Only one answer))|10 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-D) (Assertion-Reason Type Questions)|15 Videos
  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - j|3 Videos
  • MATRICES

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|3 Videos

Similar Questions

Explore conceptually related problems

By giving counter example , show that the following statements are not true : (I) In n is an odd integer, then n is prime. (ii) The equation x^(2) - 4 =0 does not a root lying between 0 and 3.

By giving a counter example,show that the following statement is false.If n is an odd integer,then n is prime.

By giving a counter example, show that the following statement is false. "If n is an odd positive integer, then n is prime."

By giving a counter example, show that the following statement is not true. p : The equation x^(2) -1=0 does not have a root lying between 0 and 2.

By giving a counter example , show that the following statements are false (i) If sqrtp is an irrational number then p is prime number (ii) Square of every rational number is greater than the number itself (iii) If all the angles of a quadrilateral is equal then it is regular

By giviing a counter example, show that the following statements are not ture. q : The equations x^(2) - 1 =0 does not have a root lying between 0 and 2.

By giving a counter example, show that the following statement are not true : The equation x^(2) - 4 = 0 does not have a root lying between 0 and 3.

By giving a counter-example, show that the following statement is false: p: If all the sides of a triangle are equal, then the triangle is obtuse angled.

For what values of a,does the equation ax^(2)-(a+1)x+3=0, have roots lying between 1 and 2.

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 x^(2)-1=0 does not have a root lying between 0 and 2.

AAKASH INSTITUTE-MATHEMATICAL REASONING-Try Yourself
  1. Which of the following sentences are statement ? (i) Cow is the onl...

    Text Solution

    |

  2. Check whether the following sentences are statement or not also provid...

    Text Solution

    |

  3. Write the negation of the following statements (i) sqrt(13) is ratio...

    Text Solution

    |

  4. Write the negation of the following statements and check whether the r...

    Text Solution

    |

  5. Find the component statement of the following compound statement , Che...

    Text Solution

    |

  6. Write the component statement of the following statement and check whe...

    Text Solution

    |

  7. For each of the following statement , determine whether an inclusive "...

    Text Solution

    |

  8. Identify the type of OR used in following statement and check whether ...

    Text Solution

    |

  9. Identify the quantifier in the following statement and write the negat...

    Text Solution

    |

  10. Rewrite the following statement with "if then" in five different ways...

    Text Solution

    |

  11. Write contrapositive of the following statement (i) If an Indian is ...

    Text Solution

    |

  12. Write the converse of the following statement (a) If H. C. F. of (a,...

    Text Solution

    |

  13. Given below are two pairs of statement , combine these two statement u...

    Text Solution

    |

  14. Check the validity of given statement (a) r : 31 is odd and prime nu...

    Text Solution

    |

  15. Check the validity of the following statement (a) p : 77 is a multip...

    Text Solution

    |

  16. (i) Check the validity of given statement r : A triangle is iosceles...

    Text Solution

    |

  17. (i) Verify by method of contradicition p : There are infinitely many...

    Text Solution

    |

  18. By giving counter example show that following statement are false (a...

    Text Solution

    |