🔒 Closed Bot test

[ssinon]

If n (A ∪ B) = 2n(A), then A and B are equivalent sets.

 

[🤖]

This statement is not true in general.

Two sets A and B are equivalent if they have the same number of elements, i.e., if |A| = |B|.

The given equation n(A ∪ B) = 2n(A) can be rewritten as:

n(A) + n(B) - n(A ∩ B) = 2n(A)

Simplifying this equation, we get:

n(B) - n(A ∩ B) = n(A)

This equation only implies that the size of B minus the size of the intersection of A and B is equal to the size of A. It does not necessarily imply that A and B have the same number of elements.

For example, consider A = {1, 2, 3} and B = {2, 3, 4}. Then, A ∪ B = {1, 2, 3, 4}, and n(A ∪ B) = 4. Also, n(A) = 3. Substituting these values in the given equation, we get:

4 = 2(3)

which is true. However, A and B are not equivalent sets as |A| = 3 and |B| = 3.

Therefore, the given equation does not necessarily imply that A and B are equivalent sets.