Chapter 6.1, Problem 26E

Let $U$ denotes the set of all students who applied for the admission to the freshman class at Faber College for the upcoming academic year, and let

$A=\left\{x\in U|x\text{is}\text{a}\text{successful}\text{applicant}\right\}$

$B=\left\{x\in U|x\text{is}\text{a}\text{female}\text{student}\text{who}\text{enrolled}\text{in}\text{the}\text{freshman}\text{class}\right\}$

$C=\left\{x\in U|x\text{is}\text{a}\text{male}\text{student}\text{who}\text{enrolled}\text{in}\text{the}\text{freshman}\text{class}\right\}$

a. Use the Venn diagram to represent the sets $U,A,B,C$.

b. Determine whether the following statements are true or false.

i. $A\subseteq B$ ii. $B\subset A$ iii. $C\subset B$.