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

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

Text Solution

AI Generated Solution

To solve the problem, we need to show two things: 1. The empty set \( \varphi \) is the identity for the operation \( ** \). 2. All elements \( A \) of \( P(X) \) are invertible with \( A^{-1} = A \). Let's go through the solution step by step. ### Step 1: Show that \( \varphi \) is the identity element for the operation \( ** \) ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|50 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 1.4|13 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise EXERCISE 13.2|18 Videos

  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 11.3|14 Videos

Similar Questions

Explore conceptually related problems

Let X be a non-empty set and let * be a binary operation on P\ (X) (the power set of set X ) defined by A*B=(A-B)uu(B-A) for all A ,\ B in P(X)dot Show that varphi is the identity element for * on P\ (X) .

Let X be a non-empty set and let * be a binary operation on P\ (X) (the power set of set X ) defined by A*B=(A-B)uu(B-A) for all A ,\ B in P(X)dot Show that varphi is the identity element for * on P\ (X) .

Define a binary operation ** on the set A={1,\ 2,\ 3,4} as a**b=a b\ (mod\ 5) . Show that 1 is the identity for ** and all elements of the set A are invertible with 2^(-1)=3 and 4^(-1)=4.

Let X be a nonempty set and *be a binary operation on P(X), the power set of X, defined by A * B=A nn B for all A, B in P(X). (

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.

Let X be a non-empty set and let * be a binary operation on P(X) (the power set of set X) defined by A*B=AuuB for all A ,\ B in P(X) . Prove that * is both commutative and associative on P(X) . Find the identity element with respect to * on P(X) . Also, show that varphi in P(X) is the only invertible element of P(X)dot

Let S be a non- empty set and P (s) be the power set of set S .Find the identity element for all union ⋃ as a binary operation on P( S) .

Let S be a non-empty set and P(s) be the power set of set S. Find the identity element for all union () as a binary operation on P(S)dot

Let S be a non-empty set and P(s) be the power set of set S. Find the identity element for all union U as a binary operation on P(S)dot