Question

if A and B are any two non empty sets and is proper subset of B if n (A) is 5 then min possible value of n(A symmetric diff. B is)

Answer 1

Ans. A is a proper subset of B

So, A∩B = A and AUB = BNow A*B = AUB/A∩B = B/A

n(A) = 5So n(B) >= 5n(A*B) = B/A

Minimum value of n(A*B) = 5/5 = 1.
(Because lowest possible value of n(B) = 5)

Where * = Symmetric difference operation, ∩ = Intersection, U = Union

Answer 2

Answer:

n(A symmetric diff. B) is 1

Step-by-step explanation:

A is a proper subset of B.

So, A ∩ B = A and A U B = B

Now, A ∆ B = A U B – A ∩ B = B – A

n(A) = 5

So, n(B) = 5 + x [Here, x is any natural no.]

n(A ∆ B) = B – A = 5 + x – 5 = x

For n(A ∆ B) to be minimum, x must also be minimum.

So, minimum value of x = 1 = n(A ∆ B).

(Note: Here ∆ represents symmetric diff.)

Hope it helps!