Home
Class 12
MATHS
Which of the following statements is a t...

Which of the following statements is a tautology ?

A

` ( ~ q ^^ p) ^^ q`

B

` ( ~ q ^^ p) ^^ ( p ^^ ~ p)`

C

(-p vv q) ^^ (-p^^q)

D

` (p ^^ q) ^^ ( ( p ^^ q) `

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` ( ~ q ^^ p) ^^ q cong ( ~ q ^^ q) ^^ p cong c ^^ p cong c`
So, Statement in option (a) is a contradiction.
` ( ~ q ^^ p) ^^ ( p ^^ ~ p) cong ( ~ q ^^ p) ^^ c cong c` , which is a contradiction
` ( ~ p vv q) ^^ ( ~ p ^^ q) cong ( ~ q ^^ p) vv t cong t`. which is a tautology,
` ( p ^^ q) ^^ ( p ^^ q) cong c` is a contradiction .
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 statement is a tautology :

Which of the following statement is a tautology?

Which of the following statement is a tautology?

Which of the following statement is a tautology? А)((prarrq)^^(~q))rarr(~p)" " B) (prarrq)^^(~q))rarr P " "C)((p rarr q)^^q))rarr(~p) " "D)((prarrq)^^q))rarr p

If p and q are two statements, then which of the following statement is a tautology

Which of the following statements is not a tautology?

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

    |