1. ## sets

for any natural number n let Bn = {x|x ε N and x ≤ n}. Describe each of the following sets in the form {x | property}

a) Bm - Bn, where m > n
b) Bm U Bn, where m ≤ n
c) Bm ∩ Bn, where m ≤ n

2. having trouble getting started, terminology is screwing me up a bit

3. Originally Posted by bretf26
for any natural number n let Bn = {x|x ε N and x ≤ n}. Describe each of the following sets in the form {x | property}

a) Bm - Bn, where m > n
b) Bm U Bn, where m ≤ n
c) Bm ∩ Bn, where m ≤ n
Maybe this will help you visualize it.

$B_m=${1,2,3...n,(n+1),(n+2),... m} and
$B_n=${1,2,3...n} when n < m

so $B_m-B_n =${(n+1),...m}

{x| n $< x \le$m}

4. I didn't mention the fact that x is an integer. (that is important)

sorry

5. for Bm U Bn, where m ≤ n

I think I understand it more, but the (n+1) confuses me a bit. Is this attempt correct at all?

Bn = {1, 2, 3...n}
Bm = {1, 2, 3...n, (n-1), (n-2)...m}

so Bm U Bn = {1....n}

{x | m ≤ x ≤ n}

6. Originally Posted by bretf26
for Bm U Bn, where m ≤ n

I think I understand it more, but the (n+1) confuses me a bit. Is this attempt correct at all?

Bn = {1, 2, 3...n}
Bm = {1, 2, 3...n, (n-1), (n-2)...m}

so Bm U Bn = {1....n}

{x | m ≤ x ≤ n}

not quite..

$B_n=${1,2,3...m,(m+1),(m+2),...n}

because m $\le$ n

$B_m=${1,2,3,...m}

This time we were asked to find the union of two sets. The union is all of the stuff in $B_n$ and all of the stuff in $B_m$

$B_n$ U $B_m=${x|1 $\le x \le$n and $x \epsilon {N}$}

7. thanks for the help, I understand it now!