Home
Class 11
MATHS
Given below are two pairs of statements....

Given below are two pairs of statements. Combine these two statements using if and only if: `p :` if the sum of the digits of a number is divisible by 3, then the number is divisible by 3. `q :` if a number is divisible by 3, then the sum of its divisible by 3.

Text Solution

Verified by Experts

A number is divisible by 3 if and only if the sum of the digits is divisible by 3.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos
  • MEASUREMENT OF ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|56 Videos

Similar Questions

Explore conceptually related problems

If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 9.

If the sum of digits of a number is divisible by three, then the number is always divisible by

If the sum of the digits in a number is a _____ of 3, then the number is divisible by 3.

If a number is divisible by 2 and 3, then it is also divisible by 6.

If a number is divisible both by 2 and 3, then it is divisible by 12.

Given below are two pairs of statements. Combine these two statements using "if and only if". (i) p: If a rectangle is a square, then all its four sides are equal. q: If all the four sides of a rectangle are equal, then the rectangle is a square. (ii) p: If the sum of digits of a number is divisible by 3, then the number is divisible by 3. q: If a number is divisible by 3, then the sum of its digits is divisible by 3.

What is the sum of the first five natural numbers divisible by 3 ?

Given below are some pairs of statements. Combine each pair using if and only if: (i) p: If a quadrilateral-is equiangular, then it is a rectangle. q: If a quadrilateral is a rectangle, then it is equiangular. (ii) p: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q: If a number is divisble by 3, then the sum of its digits is divisible by 3. (iii) p: A quadrilateral is a parallelogram if its diagonals bisect each other. q: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. (iv) p: If f(a) = 0, then (x -a) is a factor of polynomial f(x). q: If (x-a) is a factor of polynomial f(x), thenf(a) = 0. (v) p: If a square matrix A is invertible, then |A| is nonzero. q: If A is a square matrix such that |A| is nonzero, then A is invertible.

Assertion: The number 9020814' is divisible by 11. Reason: A number is divisible by 11, if the sum of its digits is divisible by 11.

RD SHARMA-MATHEMATICAL REASONING-Solved Examples And Exercises
  1. Write the component statements of each of the following statements. ...

    Text Solution

    |

  2. Given below are two pairs of statements. Combine these two statements ...

    Text Solution

    |

  3. Given below are two pairs of statements. Combine these two statements ...

    Text Solution

    |

  4. Write the following statements in the form if p then q : You can acces...

    Text Solution

    |

  5. Write each of the following statements in the form if p then q : There...

    Text Solution

    |

  6. Write the following statements in the form if p then q : It is necessa...

    Text Solution

    |

  7. Write each of the following statements in the form if p then q : It is...

    Text Solution

    |

  8. Write each of the following statements in the form if p then q : The g...

    Text Solution

    |

  9. Write the following statement in the form if p then q : It rains only...

    Text Solution

    |

  10. Write the following statement in the form if p then q : Whenever it r...

    Text Solution

    |

  11. Write the following statements in the form if p then q : It never rain...

    Text Solution

    |

  12. State the converse and contrapositive of the following statement: I...

    Text Solution

    |

  13. State the converse and contrapositive of the following statement: I ...

    Text Solution

    |

  14. State the converse and contrapositive of the following statement: A ...

    Text Solution

    |

  15. State the converse and contrapositive of the following statement: If...

    Text Solution

    |

  16. State the converse and contrapositive of the following statement: If...

    Text Solution

    |

  17. Rewrite the following statements in the form p if only ifq : if yo...

    Text Solution

    |

  18. Rewrite the following statement in the form p if only ifq : q : if ...

    Text Solution

    |

  19. Rewrite the following statement in the form p if only ifq : r : For...

    Text Solution

    |

  20. Rewrite the following statement in the form p if only ifq : If a tum...

    Text Solution

    |