Question

If A,B are non-empty sets then (A-B)union (B-A) equal​

Answer 1

Let x be any arbitrary element of (A-B) U (B-A).

Then,

=> x ∈ A-B OR  x ∈ (B-A or x ∈ A)

=> (x ∈ A or B) OR (X ∉ B or x E/ A)

=> x ∈ (A U B ) - ( A ∩ B)

Thus,

( A - B) U (B - A)  ⊆ ( A U B) - (A ∩ B)

Now,

Let y be an arbitrary element of (A U B ) - ( A ∩ B.

Then, y ∈ (A U B ) - ( A ∩ B)

y ∈ (A U B ) and y ∉ ( A ∩ B)

y ∈ A or y ∈ B) and (y ∉  A or y ∉  B)

y ∈ A or y ∉ B) and (y ∈  B or y ∉  A)

y ∈ (A - B) U (B - A )

Thus,

(A - B ) - ( A ∩ B) ⊆ (A - B ) U ( B - A )

Hence, (A U B ) - ( A ∩ B ) = (A - B ) U ( B - A)

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