Home
Class 12
MATHS
Prove that if x is odd , then x^(2) is...

Prove that if x is odd , then ` x^(2)` is also odd.

Text Solution

Verified by Experts

The correct Answer is:
`therefore` p if and only if q is true
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|20 Videos

  • MATHEMATICAL REASONING

    NEW JOYTHI PUBLICATION|Exercise QUESTION FROM COMPETITIVE EXAMS|23 Videos

  • LINEAR PROGRAMMING

    NEW JOYTHI PUBLICATION|Exercise OBJECTIVE TYPE QUESTIONS|12 Videos

  • PERMUTATIONS AND COMBINATIONS

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|63 Videos

Similar Questions

Explore conceptually related problems

Check whether the following statement is true or false by proving its contrapositive. If x, y in Ζ such that xy is odd, then both x and y are odd.

Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

Check whether the following statement is true or not. Id x, y in Z are such that x and y are odd, then xy is odd.

Check whether the statement if x and y are odd integers, then xy is an odd integer is true or false by i. direct method ii. Contrapositive method. iii. Contradiction method.

Using the words ''necessary and sufficient'' rewrite the statement ''The integer n is odd if and only if n^(2) is odd''. Also check whether the statement is true.

Write the contrapositive and converse of the following statements. If x is a prime number, then x is odd.

Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even function. Statement 2: If f^(prime)(x) is an even function, then f(x) is an odd function.

If n is odd then int_(0)^(pi//2)sin^(n)x dx is

Prove that the sum of two odd numbers is even.

Prove that x^3 + x^2 + x is factor of (x+1)^n - x^n -1 where n is odd integer greater than 3, but not a multiple of 3.

NEW JOYTHI PUBLICATION-MATHEMATICAL REASONING-QUESTION FROM COMPETITIVE EXAMS
  1. Prove that if x is odd , then x^(2) is also odd.

    Text Solution

    |

  2. The statement ~(ptoq) is equivalent to

    Text Solution

    |

  3. If p:4 is an even prime number q:6 is a divisor of 12 and r: The H...

    Text Solution

    |

  4. Which of the following is not true for any two statements p and q?

    Text Solution

    |

  5. Let p be the statement 'Ravi races' and let q be the statement 'Ravi w...

    Text Solution

    |

  6. Identify the wrong statement from the below

    Text Solution

    |

  7. Let p:7 is not greater than 4 and q: Paris is in France be two state...

    Text Solution

    |

  8. If S(p,q,r)=(~p)vv[~(q^^r)] is a compound statement, then S(~p,~q,~r) ...

    Text Solution

    |

  9. For any two statements p and q, ~(pvvq)vv(~p^^q) is logically equivale...

    Text Solution

    |

  10. Let p: roses and red and q: The sun is a star. Then the verbal transla...

    Text Solution

    |

  11. The statement pto(q to p) is equivalent to

    Text Solution

    |

  12. The negation of (pvv~q)^^q is

    Text Solution

    |

  13. Which one of the following is not a statement?

    Text Solution

    |

  14. If p:2 plus 3 is five and q: Delhi is the capital of India are two s...

    Text Solution

    |

  15. Which one of the following is a statement?

    Text Solution

    |

  16. Let p,q and r be any three logical statements. Which one of the follow...

    Text Solution

    |

  17. The truth values of p,q are r for which (p^^q)vv(~r) has truth value F...

    Text Solution

    |

  18. ~[(~p)^^q] is logically equivalent to

    Text Solution

    |

  19. The statement ~(ptoq) is equivalent to

    Text Solution

    |

  20. The statement pto(q to p) is equivalent to

    Text Solution

    |

  21. Statement-1: ~(pharr~q) is equivalent to (pharrq). Statement-2: ~(p...

    Text Solution

    |