Question

Show that a-b, b-a and a intersection b are mutually disjoint sets by giving an example

Answer 1

This is a binary operation on two sets. The elements of any disjoint union can be expressed in terms of ordered pair as (x, j), where j is the index that indicates that set where the element x came from. With the help of this operation, we can combine all the different(distinct) elements of a pair of sets. 

The disjoint union is denoted as A U* B = ( A x {0} ) U ( B x {1} ) = A* U B*

The disjoint union of sets A = ( a, b, c, d ) and B = ( e, f, g, h ) is as follows:
A* = { (a,0), (b,0), (c,0), (d, 0) } and B* = { (e,1), (f,1), (g,1), (h,1) } 
Then, 
A U* B = A* U B*
= { (a,0), (b,0), (c,0), (d, 0), (e,1), (f,1), (g,1), (h,1) } 
Examples of Disjoint SetsBack to Top
Given below are some of the examples on disjoint sets.Solved ExamplesQuestion 1: Prove that the following two sets are disjoint sets.

G = {p, q, r, s}

H = {x, y}

Solution:

The intersection of set H and set G gives an empty set. Here, set G and H does not have the elements in common with each other.

That is, G ∩∩ H = { }

Hence, the sets G and H are disjoint sets.

Question 2: Prove that Set G = {10, 12, 20, 18, 25} and set H = {11, 17, 27, 44} are disjoint sets.
Solution:

In the above problem, we have no common elements in G and H.

These elements are not intersecting of two elements.

G ∩∩ H = { }

Hence, the two sets G and H are disjoint sets.

Answer 2

Hiii. ......friend

The answer is here,

Let's take two sets,

A={1,2,3,4,5} & B={1,2,3}

A-B= {1,2,3,4,5}-{1,2,3}

=> {4,5}

B-A= {1,2,3}-{1,2,3,4,5}

=> { }

A Intersection B => {1,2,3}.

Here there is no common element in A-B , B-A & A intersection B
Hence these are mutually disjoint sets.


:-)Hope it help u.