Intersections

[Caldus]

If set A consisted of all even natural numbers (i.e. 2, 4, 6...) and set B consisted of all odd natural numbers (i.e. 1, 3, 5...), then what is the result set of:

A intersection B

Would it just be the empty set since no two natural numbers can be even and odd?

[Hurkyl]

yep

[HallsofIvy]

Yes, exactly. An element is in "A intersect B" if and only if it is in both A and B. There is no integer that is "both" even and odd and so, in this case, A intersect B is empty. That's a very common occurence. In fact there's a special name for it: the two sets are "disjoint".

[himanshu121]

Yes it should be null set

[Caldus]

I was kind of nervous when I was taking a test on this material because the question was to list at least three elements that were in the following sets, and one of those following sets was A intersection B. Guess it had to be a typo on the test. Hopefully I didn't read the question wrong. If I remember right, I'm very sure that A and B were natural number sets. Ah well.

Thanks.