Home
Class 11
MATHS
If R is the set of all real numbers. wha...

If R is the set of all real numbers. what do the cartesian products `R xx R` and `R xx R xx R` represent ?

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|348 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

Similar Questions

Explore conceptually related problems

If R is the set of real numbers and Q is the set of rational numbers, then what is R-Q?

Show that the function f : R_* rarr R_* defined by f (x) = 1/x is one-one and onto, where R_* is the set of all non-zero real numbers. Is the result true, if the domain R_* is replaced by N with co-domain being same as R_* ?

Let S be the set of all real numbers and let R be the relation in S defined by R = {(a,b), a leb^2 }, then

Let R be the set of real numbers. Define a real function f : R rarr R by f (x) =x + 10 . Sketch the graph of this function.

Let R be the set of all real numbers. Let f: R rarr R be a function such that : |f(x) - f(y)|^2 le |x-y|^2, AA x, y in R . Then f(x) =

Let N be the set of all natural numbers and R be a relation in N defined by : R = {(a, b) : a is a factor of b} Show that R is reflexive and transitive.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxxNdot

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Show that zero is the identity for addition on R and 1 is the identity for multiplication on R. But there is no identity element for the operations – : R xx R rarr R and -: R_* xx R_* rarr R_*

Show that the relation R in the set R of real numbers defined as R = {(a, b) : a le b} , is reflexive and transitive but not symmetric.

MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. The Cartesian product A xx A has 9 elements among which are found (-1,...

    Text Solution

    |

  2. If A= {-1, 1}, find A xx A xx A.

    Text Solution

    |

  3. If R is the set of all real numbers. what do the cartesian products R ...

    Text Solution

    |

  4. If A xx B = {(a, x).(a , y). (b, x), (b, y)}. Find A and B.

    Text Solution

    |

  5. If A = { 1, 2}, B = {3, 4}, C = {4, 5}, find A xx (B uu C).

    Text Solution

    |

  6. If A={a, b,c}, B= {c, d} and C= {d, e, f}, find : (A nn B)xxC.

    Text Solution

    |

  7. If A={a, b,c}, B= {c, d} and C= {d, e, f}, find : (A xx B) nn (BxxC).

    Text Solution

    |

  8. Let A = {1, 2, 4}, B= {3, 5, 7} and C = {5, 7, 9}, find A xx (B nn C).

    Text Solution

    |

  9. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

    Text Solution

    |

  10. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

    Text Solution

    |

  11. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : Axx (B uu C).

    Text Solution

    |

  12. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

    Text Solution

    |

  13. Let A = {2, 4, 6}, B= {6, 8, 10} and C = {10, 12,14}. Find B xx (A uu ...

    Text Solution

    |

  14. Let A = {1/2,2}, B = {2,3,5}, C= {-1,- 2}. Verify that : A xx (B nn C)...

    Text Solution

    |

  15. Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y...

    Text Solution

    |

  16. The Cartesian product A xx A has 9 elements among which are found (-1,...

    Text Solution

    |

  17. Let A = {1, 2, 3}, B= {2, 3, 4} and C= {4, 5}. Verity that : A xx (Buu...

    Text Solution

    |

  18. If A= {1, 2, 3}, B= {4},C = {5}. then verify that : A xx (Buu C)= (A ...

    Text Solution

    |

  19. If A= {1, 2, 3}, B= {4},C = {5}. then verify that : A xx (B nn C)= (A...

    Text Solution

    |

  20. If A= {1, 2, 3}, B= {4},C = {5}. then verify that : A xx (B - C)= (A ...

    Text Solution

    |