show that the ways to pick 2 subsets A and B of [n] when A is subset of B equals to n^3

Question

I know that the total of subsets of a set is 2^n. I am assuming I have to use combinations but I cannot think of something to start. Anybody can help Thanks in advance

Welcome to MSE. Please use mathjax to write your questions. – jjagmath Dec 09 '20 at 22:10 — jjagmath, Dec 09 '20 at 22:10
BTW, the answer is not $n^3$, as the title say, is $3^n$ – jjagmath Dec 09 '20 at 22:14 — jjagmath, Dec 09 '20 at 22:14

score 0 · Accepted Answer · answered Dec 09 '20 at 22:09

0

For each element of $[n]$ you have $3$ choices:

Put it in $A$ (so necessarily also in $B$).
Put it in $B$ but not in $A$.
Don't put it in $A$ nor $B$.

answered Dec 09 '20 at 22:09

jjagmath

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show that the ways to pick 2 subsets A and B of [n] when A is subset of B equals to n^3

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