Chapter 2.1, Problem 5E

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

(a) $3\in \left\{1,3,5\right\}$

(b) $\left\{3\right\}\in \left\{1,3,5\right\}$

(c) $\left\{3\right\}\underset{\ne }{\subset }\left\{1,3,5\right\}$

(d) $\left\{3,5\right\}\cancel{\subseteq }\left\{1,3,5\right\}$

(e) $\left\{1,3,5\right\}\underset{\ne }{\subset }\left\{1,3,5\right\}$

(f) $1\in \left\{a+2b|a,b\text{ even intergers}\right\}$

(g) $0\in \left\{a+b\sqrt{2}|a,b\in Q,b\ne 0\right\}$