In russels paradox we say that a set of cars does not belong to itself?how do we justify that?

Answer 1

The set of cars is not a car.

Answer 2

Look at it this way:

Suppose you compose a list of all of the books ever printed that do not contain their title somewhere in its text (not including cover, title page, etc. just the main text).

At this point, there is nothing amiss. But suppose that the list gets so long that you decide to make the list into a book, and you give this book a title.

Now, there's a dilemma that did not exist when the book was merely a list: do you include the title this book IN the book, as one of the books that doesn't contain its title?

If you do, then the book contains its title, and it should not be included.

If you don't, then the book is incomplete, for it does not list ALL books that do not contain their titles.

The paradox arises when you make the container the same type of object as the objects that it contains.

Answer 3

if S= set of cars,
then S is not an element of S, since S itself is NOT a car, but a set.