1. ## Sets

Couple set questions..

1.) Given:

{x | x = k^2, k=1,2,3,...,100}, determine the cardinal #.

I said it would be 100, as you'd have 100 numbers.

2.) Suppose D is a proper subset of E;

Determine the least possible # of elements that are in D.

I'm assuming this is 1?

3.) If D is a subset of E, are we able to say D is a proper subset of E?

I'd say NO but my example I tried given contradicted itself.

2. Originally Posted by DiscreteW
Couple set questions..

1.) Given:

{x | x = k^2, k=1,2,3,...,100}, determine the cardinal #.

I said it would be 100, as you'd have 100 numbers.
yes

2.) Suppose D is a proper subset of E;

Determine the least possible # of elements that are in D.

I'm assuming this is 1?
note that the empty set is a subset of any set, except perhaps the empty set ...now there's some food for thought

3.) If D is a subset of E, are we able to say D is a proper subset of E?

I'd say NO but my example I tried given contradicted itself.
i wrote nonsense here, see my next post

EDIT: see red

3. So um for 2 the least number would be nothing? The null set? Or 1? Or no possible answer?

4. Originally Posted by DiscreteW
So um for 2 the least number would be nothing? The null set? Or 1? Or no possible answer?
0 elements, since the empty set is a proper subset

and for question 3, i read something incorrectly. the answer is still "no" though, but for a different reason. namely, a set is a subset of itself