Chapter 2.1, Problem 7E

Determine which of the following are true and which are false. Justify your answers.

(a) $\varnothing \subseteq \varnothing$

(b) $\varnothing \subseteq \{\varnothing \}$

(c) $\varnothing \in \varnothing$

(d) $\varnothing \in \{\varnothing \}$

(e) $\left\{1,2\right\}\cancel{\subseteq }\left\{1,2,3,\left\{1,2,3\right\}\right\}$

(f) $\left\{1,2\right\}\in \left\{1,2,3,\left\{1,2,3\right\}\right\}$

(g) $\left\{1,2\right\}\underset{\ne }{\subset }\left\{1,2,\left\{\left\{1,2\right\}\right\}\right\}$

(h) $\left\{1,2\right\}\in \left\{1,2,\left\{\left\{1,2\right\}\right\}\right\}$

(i) $\left\{\left\{1,2\right\}\right\}\subseteq \left\{1,2,\left\{1,2\right\}\right\}$