Home
Class 12
MATHS
Which of the following is a tautology ?...

Which of the following is a tautology ?

A

`p to ( p to q)`

B

` ( p vv q) to p`

C

` p vv ( p vv q)`

D

` ( p vv q) to q`

Text Solution

Verified by Experts

we know that ` p to q = ~ p vv q `
` p to ( p to q) = ~ ( p vv q) = ~ p vv ( ~ p vv q) = ~ p vv q`
` ( p vv q) to p = ~ ( p vv q) vv p = ( ~ p ^^ ~ q) vv p = ( ~ p vv q) vv p = ( ~ p vvp) ^^ ( ~ q vv p)`
` t ^^ ( ~ q vv p) = ~ q vv p`
` p vv ( p to q ) = p vv ( ~ p vvq) = (-p vv ~ p) vv q = t vv q= t`
Hence, `p vv (p to q) ` is a tautology .
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

Which of the following is tautology

Which of the following is tautology

Which of the following is tautology?

Which of the following is not a tautology.

Which of the following is not a tautology?

If q is false and (p^^q)harr r is also true then which of the following are tautology (A) (p vv r)rarr(p^^r)(B)(p vv r)(C)(p^^r)rarr(p vv r)(D)p^^r

The statement among the following that is a tautology is :

The only statement among the following that is a tautology is

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

OBJECTIVE RD SHARMA-MATHEMATICAL REASONING -Section I - Solved Mcqs
  1. The contrapositive of p to ( ~ q to ~ r) is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Which of the following is wrong?

    Text Solution

    |

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

    Text Solution

    |

  7. Which of the following statements is a tautology ?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Which of the following is a tautology ?

    Text Solution

    |

  20. The proposition ~p vv( p ^^ ~ q) is equivalent to

    Text Solution

    |