Home
Class 12
MATHS
If the inverse of implication p rarr q i...

If the inverse of implication `p rarr q` is defined as `~p rarr ~q`, then the inverse of the proposition `(p ^^ ~q) rarr r` is not equivalent to :
I : `~r rarr `p vv q`
II : `~p vv ~q rarr ~r`
III : `r rarr p ^^ ~q`
The true statements in the above are :

A

I, II only

B

II, III only

C

I, III only

D

All the above

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    AAKASH SERIES|Exercise Practice Exercise|21 Videos
  • LOGARITHMIC SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos
  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise EXERCISE|28 Videos

Similar Questions

Explore conceptually related problems

The inverse of the proposition (p ^^ ~q) rarr r is

p ^^ (~q) rArr p is

p rArr p vv q is

The contra positive of (~p ^^ q) rarr ~r is

p rarr q is logically equivalent to

The contrapositive of (p vv q) rarr r is

Statement p rarr (q rarr p) is equivalent to

AAKASH SERIES-MATHEMATICAL REASONING -Practice Exercise
  1. If the inverse of implication p rarr q is defined as ~p rarr ~q, then ...

    Text Solution

    |

  2. Which of the following is a proposition

    Text Solution

    |

  3. Let p and q be two proposition given by p : I play cricket during th...

    Text Solution

    |

  4. If x = 5 and y = -2, then x - 2y = 9. The contrapositive of this propo...

    Text Solution

    |

  5. Consider the proposition : "If we control population growth, then we p...

    Text Solution

    |

  6. Consider the following propositions p : I have the raincoat. q : I...

    Text Solution

    |

  7. p rarr q is logically equivalent to

    Text Solution

    |

  8. The contrapositive of p rarr (~q rarr ~r) is

    Text Solution

    |

  9. The negation of p ^^ ~(q ^^ r) is

    Text Solution

    |

  10. The contra positive of (~p ^^ q) rarr ~r is

    Text Solution

    |

  11. Which of the following is logically equivalent to (p ^^ q) ?

    Text Solution

    |

  12. (p ^^ ~q) ^^ (~p vv q) is

    Text Solution

    |

  13. Which of the following is always true ?

    Text Solution

    |

  14. Which of the following propositions is a tautology ?

    Text Solution

    |

  15. Which of the following proposition is a tautology ?

    Text Solution

    |

  16. Observe the following statements I : The dual of [ ~p ^^ q)] vv [ p...

    Text Solution

    |

  17. Match the duals of t he statements in List - I : {:(,"List - I",,"Li...

    Text Solution

    |

  18. Match the duals of the statements in list - I : {:(,"List - I",,"Lis...

    Text Solution

    |

  19. Observe the following statements : Statements - I : (p vv q) ^^ (~p ...

    Text Solution

    |

  20. Observe the following statements Statement - I : p vv ~(p ^^ q) is a...

    Text Solution

    |

  21. Consider the following two statements P :if 7 is an odd number, then...

    Text Solution

    |