Home
Class 12
MATHS
The contrapositive of p to ( ~ q to ~ r...

The contrapositive of ` p to ( ~ q to ~ r) ` is

A

` ( ~q ^^ r) to ~ p `

B

` ( q ^^ ~ r) to ~ p`

C

` p to ( ~ r vv q)`

D

` p ^^ ( q vv r)`

Text Solution

Verified by Experts

The correct Answer is:
A
we know that dthe contrapositive of ` p to q " is " ~ q to ~ p` . Threrefore, contrapositive of `p to ( ~ q to ~ r) " is " ~ ( ~ q to ~ r) to ~ p `
` or , ( ~ q ^^ r) to ~ p `
[ `~ ( p to q) cong p ^^ ~ q `
` ~ ( ~ q to ~ r) cong ~ q ^^ r ` ]
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|4 Videos

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Exercise|40 Videos

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Solved MCQs|5 Videos

  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA|Exercise Exercise|30 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Contrapositive of p to q is

The contrapositive of (~p ^^ q) to ~r is

The contrapositive of p to ~q is -------

The contrapositive of (pvvq) to r is

The contrapositive of (p vv q)to r is

The contrapositive of p implies ~q is

The contrapositive of inverse of p to ~ q is

The contrapositive of p rarr(sim q rarr sim r) is

OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. The negation of the propostion " if a quadrillatcral is a square, then...

    Text Solution

    |

  2. The contrapositive of (pvvq) to r is

    Text Solution

    |

  3. The contrapositive of p to ( ~ q to ~ r) is

    Text Solution

    |

  4. The contrapositive of the statement "if 2^(2) =5 then I get first cla...

    Text Solution

    |

  5. If x = 5 nad y = -2 , then x -2y =9, the contrapositive of this propos...

    Text Solution

    |

  6. The diagonals of a rhombus are perpendicular. The contrapositive of th...

    Text Solution

    |

  7. Which of the following is wrong?

    Text Solution

    |

  8. The symbolic form of logic of the circuit given below is : (RDSMATH...

    Text Solution

    |

  9. Which of the following statements is a tautology ?

    Text Solution

    |

  10. The statement p to(q to p) is equivalent to

    Text Solution

    |

  11. Let S be non-empty subset of R. consider the following statement: P:...

    Text Solution

    |

  12. Consider the following statements P: Suman is brilliant Q: Suman i...

    Text Solution

    |

  13. The only statement among the following i.e. a tautology is

    Text Solution

    |

  14. Let p and q be two statements. Amongst the following , the statement t...

    Text Solution

    |

  15. The statement ~(p harr ~q) is

    Text Solution

    |

  16. The negation of ~ svv(~ r^^s) is equivalent to :

    Text Solution

    |

  17. The Bolean Expression ( p ^^ ~ q) vv q vv ( ~ p ^^ q vv ( ~ p ^^ q) ...

    Text Solution

    |

  18. Consider the following statements. p : if 7 is an odd number , then ...

    Text Solution

    |

  19. The negation of A to (A vv ~ B) is

    Text Solution

    |

  20. The following statement (p to q) to [(~p to q) to q] is

    Text Solution

    |