Question

Prove that
A- B = A delta ( A intersection B)

Answer 1

Step-by-step explanation:

Prove that AΔB=(A∖B)∪(B∖A)

The set AΔB consists of those elements that belong to exactly one of the sets A , B . Thus AΔB=(A∪B)∖(A∩B) .

We show that AΔB=(A∖B)∪(B∖A) , by showing that each set is contained in the other.

Let x∈AΔB . Then x∈A , x∉B or x∈B , x∉A . In the first case, x∈A∖B , and in the second case x∈B∖A . In any case, x∈(A∖B)∪(B∖A) .

Now let x∈(A∖B)∪(B∖A) . Then x∈A∖B or x∈B∖A . In the first case, x∈A , x∉B , and in the second case, x∈B , x∉A . Therefore x is in exactly one of the sets A , B . Hence x∈AΔB .

This proves AΔB=(A∪B)∖(A∩B).

hope this helps you..plzz Mark as BRAINLIEST answer ❤

Answer 2

Step-by-step explanation:

The set AΔB consists of those elements that belong to exactly one of the sets A , B . Thus AΔB=(A∪B)∖(A∩B) .

We show that AΔB=(A∖B)∪(B∖A) , by showing that each set is contained in the other.

Let x∈AΔB . Then x∈A , x∉B or x∈B , x∉A . In the first case, x∈A∖B , and in the second case x∈B∖A . In any case, x∈(A∖B)∪(B∖A) .

Now let x∈(A∖B)∪(B∖A) . Then x∈A∖B or x∈B∖A . In the first case, x∈A , x∉B , and in the second case, x∈B , x∉A . Therefore x is in exactly one of the sets A , B . Hence x∈AΔB .

This proves AΔB=(A∪B)∖(A∩B). ■