I am unable to understand the following question and its solution related to "sets".Please explain it for me.Question-Let A, B and C be three sets....

The given proposition that is A o B and B 0C is true ,
then A o C need not be true.

We opt for to be & (
meaning intersection in set language).

Example : A = {1, 2
, 3} , B = { 1,2,3,4,5}, C = {4,5, 67}.

Then A & B
= {2,3} is true. Or A intersects B is true.

 B & C
= {4,5} is true . Or B intersets C is true.

But the A
intersects B and Bintersects C are both true inthe example. But this does mean  or imply
A intersets C. So A& C is false.

Given solution in
the posted problem:

A = {1}

B=
{{1}, 2} is not correct. {1} is a set and can not be an element
.

C = { {1}, 2, 3}. The defintion of this set is not
correct. {1} is a set . 2 and 3 are elements.

A set of sets
is a class. So B and C are neither sets nor classes.