Question

prove that A-B and A ∩ B are mutualy disjoint .

Answer 1

Answer:

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