Question

prove that (A-B) U (B-A) =(A U B) - (A intersection B)

Answer 1

Answer:

We have to prove that : (A-B) U (B-A) = (A∪B) - (A∩B)

Proof:

Let,  x ∈ (A-B) U (B-A)

⇒ x ∈ (A-B) or x ∈ (B-A)

⇒  x ∈ A But x ∉ B  or  x ∈ B but x ∉ A,

⇒ x ∈ A or x ∈ B

⇒ x ∈ (A∪B)

⇒ x ∈ (A∪B) - (A∩B)

Since here x represents the arbitrary element of the set (A-B) U (B-A).

Thus, (A-B) U (B-A) = (A∪B) - (A∩B)

Hence, proved.

Answer 2

Answer:

Concept:

Set is a very fundamental idea. It is simple, but it is sufficient as the foundation for all abstract mathematical concepts. The elements of a set define it. We write xA to say that x is an element of A if A is a set. Sets are groupings of well-defined objects; relations are the connections between people from two sets A and B; and functions are a special sort of relation in which each element in A has exactly (or at most) one relationship with an element in B.

Given:

Prove that (A-B) U (B-A) =(A U B) - (A ∩ B) by using formula​

Find:

find the solution for the given question

Answer:

The group of people or items that are included in either set X or set Y, or both, is defined as the union of two sets X and Y. The set of elements that belong to both sets X and Y is defined as the intersection of two sets X and Y. The symbol represents the joining of two collections of data.

Let ,

$X$ ∈ $(A-B) U (B-A)$

$X$ ∈ $(A-B)$ $or$ $X$ ∈ $(B-A)$

$X$ ∈ $A$ but $X$ ∉ $B$ or $X$ ∈ $B$ but $X$ ∉ $A$

$X$ ∈ $A$ or $X$ ∈ $B$

$X$ ∈ $(AUB)$

$X$ ∈ $(AUB) - (A$ ∩ $B)$

Because x denotes any arbitrary element of the collection

$(A-B) U (B-A)$

Thus ,

$(A-B) U (B-A) = (AUB) - (A$ ∩ $B)$

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