# Homework Help: Scalar multiplying a set?

1. Dec 5, 2012

### V0ODO0CH1LD

Scalar multiplying a set??

1. The problem statement, all variables and given/known data

Let A and B be two finite non-empty sets such that A $\subset$ B and n({C : C $\subset$ B\A}) = 128. Then what is the value of n(B) - n(A)?

2. Relevant equations

3. The attempt at a solution

I actually got to 7 by assuming that n was multiplying the cardinality of C, but I am not sure if that is what happens. What does it mean to have a scalar multiplying a set? Or is n not a scalar in this case?

2. Dec 5, 2012

### Staff: Mentor

Re: Scalar multiplying a set??

I don't read this as "n times a set" but as "the number of elements in set <whatever>". Check your book or notes for exactly what this notation means.

3. Dec 5, 2012

### V0ODO0CH1LD

Re: Scalar multiplying a set??

That actually makes a lot of sense! I checked my book and n(A) is a notation for the cardinality of A. But the funny thing is that the answer would still be 7, even though I carried the notation around as if it were a multiplication.

If C = P(B\A) where P(B/A) is the power set of B\A. Then n(C : {C $\subset$ A\B}) = P(B\A) = 2n(B\A) = 128 = 27.

Therefore n(B\A) = 7.

n(B\A) = n(B) - n(A) if A $\subset$ B.

Is that still correct?

4. Dec 5, 2012

### Dick

Re: Scalar multiplying a set??

Yes, it is. I'm not sure how you got it by misunderstanding the notation, but ok.