Question

explain symmetric different of two non empty sets with illustration?

Answer 1

Answer:

The symmetry difference of two non - empty set S and T is defined by

Answer 2

Concept:

The group of elements that are present in both sets $A$ and $B$, but not in their intersection, makes up the symmetric difference between the two sets. The items in $A$ or $B$ but not in both $A$ and $B$ make up the symmetric difference between the sets $A$ and $B$. Although there are other notations for the symmetric difference, we shall express it as $A B$. We will look at the sets $A = 1,2,3,4,5$ and $B = 2,4,6$ as an illustration of the symmetric difference.

Given:

Here it is given that the question is explain symmetric different of two non empty sets with illustration.

Find:

We have to find an explain symmetric different of two non empty sets with illustration.

Solution:

According to the question, Let us recall that the symmetric difference is defined as

$A$△$B=(A$∖$B)$∪$(B$∖$A)$

Thus, if $B$ was not empty, it would contain an element b. I distinguish two cases:

If b also lies in $A$, then by hypothesis it lies in $A$△$B=A.$ This is absurd, because $A$△$B$ does not contain any element of $A$∩$B.$

If $b$ does not lie in $A$, then it lies in $B$∖$A$. Hence, by definition, it must lie in $A$△$B$. But by hypothesis, this is no other than $A$, which leads us to an absurdity.

We conclude that $B$ must be empty.

Hence, we have explain symmetric different of two non empty sets with illustration and this is our final answer also.

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