Question

If A and B be two sets such that n(A) =15,n(B)=25,then number of possible values of symmetric difference of A and B

Answer 1

Answer:

Hence, the possible values of symmetric difference of A and B is:

$10\leq n(B-A) \leq 25$

Step-by-step explanation:

We can get the maximum value of the symmetric difference if B is not contained in A or A is not contained in B.

i.e. we can say that intersection of A and B is zero.

Hence,

$n(B-A)=n(B)-n(A\bigcap B)\\\\n(B-A)=25-0=25$

Similarly we get the least possible value when A is completely contained in A so that:

$n(B-A)=n(B)-n(A\bigcap B)\\\\n(B-A)=25-15=10$

Hence, the possible values of symmetric difference of A and B is:

$10\leq n(B-A) \leq 25$