Home
Class 12
MATHS
Given a non-empty set X, let **: P(X) xx...

Given a non-empty set X, let `**: P(X) xx P (X) to P (X)` be defined as `A **B = (A-B) uu (B-A) , AA A, B in P (X).` Show that the empty set `phi` is the identity for the opertion `**` and all the elements A of `P (X)` are invertible with `A ^(-1) =A.`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise EXERCISE 1.4|13 Videos

  • PROBABILITY

    NCERT TELUGU|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • VECTOR ALGEBRA

    NCERT TELUGU|Exercise Miscellaneous Exercise on chapter 10|17 Videos

Similar Questions

Explore conceptually related problems

Let X be a non empty set. Let P(X) be the power set of X. Define *: P(X) * P(X) to P(X) by A * B =(A-B) cup (B-A), AA A, B in P(X) . Find the identity element and inverse element of A.

If P(A) = 3/4 , P(B) = 2/5 , P(Ann B) = 1/4 then P(A uu B) =

B={x:x+5=5} is not an empty set. Why?

The zero of p(x)=ax+b is

If P(A) = 0.25 , P(B) = 0.5 , P(A nn B) = 0.16 then find P(A uu B) .

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

Suppose X ~ B(n,p) and P(X=3) = P(X=5) . If P gt (1)/(2)

NCERT TELUGU-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

    Text Solution

    |

  2. Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if ...

    Text Solution

    |

  3. If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

    Text Solution

    |

  4. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

    Text Solution

    |

  5. Show that the function f: R to R given by f (x) = x ^(3) is injective...

    Text Solution

    |

  6. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

    Text Solution

    |

  7. Give examples of two functions f : N to N and g : N to N such g o f is...

    Text Solution

    |

  8. Given a non empty set X, consider P (X) which is the set of all subset...

    Text Solution

    |

  9. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

    Text Solution

    |

  10. Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S...

    Text Solution

    |

  11. Consider the binary opertions **: R xx R to R and o : R xx R to R defi...

    Text Solution

    |

  12. Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as ...

    Text Solution

    |

  13. If A = {0,1,2,3,4,5} Define a binary operation * on A as a*b = {{:(a+b...

    Text Solution

    |

  14. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

    Text Solution

    |

  15. Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) w...

    Text Solution

    |

  16. Let A = {1,2,3}. Then number of equivalence relations containing (1,2)...

    Text Solution

    |

  17. Let f : R to R be the Signumb Function defined as f (x) = {{:(1",",...

    Text Solution

    |

  18. Number of binary opertions on the set {a,b} are

    Text Solution

    |