set theory: $A = \{3r+5s+8t \mid r,s,t \in\mathbb N, r = s + t\}$ and $C = \{n \in\mathbb N\mid 0 \le \le 12\}$. Find $A\cap C$

Question

Can someone kindly explain this question to me, I am not sure how to do this.

My approach: Since for Set $A = (r = S + T)$

$A = \{ 8s + 11t\mid s,t \in\mathbb N\}$

$C = \{0,1,2,3,4,5,6,7,8,9,10,11,12\}$

based on the interception of these two sets, $A$ must be $0 \le 8s + 11t \le 12$

Is my approach correct, from here I calculate set $A$ elements to be $\{0,8,11\}$

Are you treating $0$ as a natural number? Also, in your definition of $C$, you wrote $nn$ where I think you meant $n$. — lulu, Jun 25 '22 at 19:39

score 1 · Answer 1 · answered Jun 25 '22 at 19:39

1

Your answer is correct. But I think in your post you mean $\mathbb{N} = \{0,1,2,...\}$. In that case there is a better notation. Use $\mathbb{Z_{\ge 0}}$ instead.

answered Jun 25 '22 at 19:39

Wang YeFei

6,390

1

He can use $\Bbb N$, this isn't the Middle Ages: it's just the internet. – Sassatelli Giulio Jun 25 '22 at 19:44
Yep I explained the issue there https://math.stackexchange.com/a/3240942/399263 – zwim Jun 25 '22 at 19:48

set theory: $A = \{3r+5s+8t \mid r,s,t \in\mathbb N, r = s + t\}$ and $C = \{n \in\mathbb N\mid 0 \le \le 12\}$. Find $A\cap C$

1 Answers1