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?

Text Solution

Verified by Experts

The Cartesian product `R xx R` represents the set `R^(prime) xx R=(x, y): x, y in R` . which repre sents the coordinates of all the points in two dimensional space and the cartesian product `R xx R xx R` represents.the set `R xx R xx R=(x, y, z): x, y, z in R`. which represents the coordinates of all the points in three - dimensional. space.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|89 Videos
  • SEQUENCES AND SERIES

    V PUBLICATION|Exercise QUESTIONBANK|140 Videos

Similar Questions

Explore conceptually related problems

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

Let R be the set of all real numbers and let f:R rarr R be a function defined by f(x) = x +1 Complete the following table

Let R be the set of all real numbers and let f:R rarr R be a function defined by f(x) = x +1 Draw the graph f

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 R be the set of all real numbers. If , f : R to R be a function such that |f (x) - f (y) | ^(2) le | x -y| ^(3), AA x, y in R, then f'(x) is equal to a)f (x) b)1 c)0 d) x ^(2)

Let R be the set of real numbers. Define the real function. f: R rarr R by f(x)=x+1 0 and sketch the graph of this function.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find R.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find range of R.

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTIONBANK
  1. Let A={1,2,3},B={3,4} and C={4,5,6}. Find Axx(BnnnC)

    Text Solution

    |

  2. Let P={1,2}.Find PxxPxxP

    Text Solution

    |

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

    Text Solution

    |

  4. If (x/3+1,y-2/3)=(5/3,1/3), find the values of x and y.

    Text Solution

    |

  5. If A xx B={(p, q),(p, r),(m, q),(m, r)}, fịnd A and B

    Text Solution

    |

  6. If the set A has 3 elements and the set B = {3,4,5}, then find the num...

    Text Solution

    |

  7. If G = {7,8} and H ={5,4,2}, find Gxx H and H xx G

    Text Solution

    |

  8. State whether each of the following statetments is true or false. If t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Let A={1,2},B={1,2,3,4},C={5,6} and D={5,6,7,8}.Verify that Axx(Bn...

    Text Solution

    |

  12. Let A = {1,2} and B = {3,4}. Write A xx B. How many subsets will A xx...

    Text Solution

    |

  13. Let A and B are two sets such that n (A) = 3 and n (B) = 2. If (x,1),...

    Text Solution

    |

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

    Text Solution

    |

  15. Let A={1,2,3,4,5,6} be a set. Defined a relation R from A to A by R={(...

    Text Solution

    |

  16. A={1,2,3,……,14}. R is a relation from A to A defined by R={(x,y): 3x-y...

    Text Solution

    |

  17. A relation R on set natural numbers is defined by R={(x,y):y=x+5,x is ...

    Text Solution

    |

  18. A = {1,2,3,5} and B = {4,6,9}. Define a relation R from A to B by R =...

    Text Solution

    |

  19. Shows a relationship between the sets P and Q. write this relation ros...

    Text Solution

    |

  20. Let A={1,2,3,4,6}.Let R be the relation on A defined by R={(a,b):a,b...

    Text Solution

    |