Question

Verify whether $A\subset B$ for the sets $A=\left\{\{a,b,c\}\right\},B=\{1,\{a,b,c\},2\}$

Answer 1

The set $A=\left\{\{a,b,c\}\right\}$ means that $A$ is the set containing the set $\{a,b,c\}$ as its only element.

The definition of $A\subset B$ means that whenever $a$ is an element of $A$, we have that $a$ is also an element of $B$.

So by taking every element of the set $A$ we see that it is an element of $B$. The only element of $A$ is $\{a,b,c\}$.

$\therefore A\subset B$