Home
Class 11
MATHS
Are the following pairs of statements ne...

Are the following pairs of statements negations of each other?
The number x is a rational number.
The number x is an irrational number.

Text Solution

Verified by Experts

The negation of the first statement is . .(x)^(top). .is an irrational nụmber which is the second statement. Therefore the pairs are negations of each ather.
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUALITIES

    V PUBLICATION|Exercise QUESTIONBANK|95 Videos
  • PERMUTATIONS AND COMBINATIONS

    V PUBLICATION|Exercise QUESTIONBANK|79 Videos

Similar Questions

Explore conceptually related problems

Are the following pairs of statements negations of each other The number x is not a rational number The number x is not an irrational number

Are the following pairs of statements negátions of each other: i) The number x is not a rational number. The number x is not an irrational number.

Check whether the following pair of statements are negation of each other Give reasons for your answer. i)x+y=y+x is true for every real number x and y. (ii)There exist a real number x and y for which x+y = y+x.

Check whether the following pair of statements are negation of each other. Give reasons for your answer. i) x+y=y+x is true for every real numbers x and y ii) There exists real numbers x and y for which x+y=y+x

Identify the type of 'OR' used in the following statement and check whether the statements are true or false:(i) sqrt 2 is a rational number or an irrational number.

Check whether the following pair of statements are negation of each other.Give reasons for your answer.(ii)There exists real numbers x and y for which x+y=y+x .

Check whether the following pair of statements are negation of each other.Give reasons for your answer.(i) x+y=y+x is true for every numbers x and y.

Find the intersection of the following pairs of sets and and find if they are disjoint sets? E={x:x is an odd natural number}, F={x:x is an even natural number}.

(a)Check the validity of the statement given below by contradiction method."The sum of an irrational number and a rational number is irrational".

(a)Check the validity of the statement given below by contradiction method.'P:The sum of an irrational number and a rational number is irrational".

V PUBLICATION-MATHEMATICAL REASONING-QUESTION BANK
  1. Write the negation of the following statement: every natural number ...

    Text Solution

    |

  2. Are the following pairs of statements negátions of each other: i) The...

    Text Solution

    |

  3. Are the following pairs of statements negations of each other? The num...

    Text Solution

    |

  4. Find the component statements of the following compound statements and...

    Text Solution

    |

  5. Find the component statements of the following compound statements and...

    Text Solution

    |

  6. Write the component statements of the following compound statements an...

    Text Solution

    |

  7. For each of the following statements, determine whether an inclusive O...

    Text Solution

    |

  8. For the following compound statement first identify the connecting wor...

    Text Solution

    |

  9. For the following compound statement first identify the connecting wor...

    Text Solution

    |

  10. For the following compound statement first identify the connecting wor...

    Text Solution

    |

  11. For the following compound statement first identify the connecting wor...

    Text Solution

    |

  12. Identify the quantifier in the following statements and write the nega...

    Text Solution

    |

  13. Check whether the following pair of statements are negation of each ot...

    Text Solution

    |

  14. Write the contrapositive and converse of the following statement: 'If ...

    Text Solution

    |

  15. Write the converse of the following statements. (i) If a number n is ...

    Text Solution

    |

  16. For each of the following compound statements, first identify the corr...

    Text Solution

    |

  17. Given below are two pairs of statements. Combine these two statements ...

    Text Solution

    |

  18. Rewrite the following statement with "If -then" in five different ways...

    Text Solution

    |

  19. Write the contrapositive and converse of the following statement: If...

    Text Solution

    |

  20. Write the contrapositive and converse of the following statement: If...

    Text Solution

    |