Help with intro to Set Theory

Question

^ That's the problem, but I'd also like to know why...

I have:

a. True

b. True

c. False, because you'd need to have a set with the null set in it on the right hand side.

d. True, seems like what was missing from c

e. True

f. True

g. True

Thanks!

Answer 1

Hint:

• When $a\in A$ then you can find easily $a$ among the other elements of the set $A$.

So, for example $a$ and $b$ are true because you can easily find the element $\emptyset$ in both $\{\emptyset\},\{\emptyset,\{\emptyset\}\}$. While $c$ is wrong, since $\{\emptyset\}$ is not an element of itself.

• When $a\in A$ then we always have $\{a\}\subset A$

So, for example, $f$ is correct. Because in it we see that $\{\emptyset\}\in\{\emptyset,\{\emptyset\}\}$ and so we have $$\{\{\emptyset\}\}\subset\{\emptyset,\{\emptyset\}\}$$