Chapter 13.1, Problem 10AYU

To determine

To write: All the subsets of $\{a,b,c,d,e\}$.

Answer to Problem 10AYU

$\varphi$, $\left\{a\right\},\left\{b\right\},\left\{c\right\},\{d,\left\{e\right\}$, $\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{a,e\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{b,e\right\},\left\{c,d\right\},\left\{c,e\right\},\left\{d,e\right\}$, $\left\{a,b,c\right\},\left\{a,b,d\right\},\left\{a,b,e\right\},\left\{a,c,d\right\},\left\{a,c,e\right\},\left\{a,d,e\right\},\left\{b,c,d\right\},\left\{b,c,e\right\},\left\{b,d,e\right\},\left\{c,d,e\right\}$, $\left\{a,b,c,d\right\},\left\{a,b,c,e\right\},\left\{a,b,d,e\right\},\left\{a,c,d,e\right\},\left\{b,c,d,e\right\}$, $\left\{a,b,c,d,e\right\}$

Explanation of Solution

Given:

The set $\{a,b,c,d,e\}$.

The subsets are,

Zero element - $\varphi$.

One element - $\left\{a\right\},\left\{b\right\},\left\{c\right\},\left\{d\right\},\left\{e\right\}$.

Two elements - $\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{a,e\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{b,e\right\},\left\{c,d\right\},\left\{c,e\right\},\left\{d,e\right\}$.

Three elements - $\left\{a,b,c\right\},\left\{a,b,d\right\},\left\{a,b,e\right\},\left\{a,c,d\right\},\left\{a,c,e\right\},\left\{a,d,e\right\},\left\{b,c,d\right\},\left\{b,c,e\right\},\left\{b,d,e\right\},\left\{c,d,e\right\}$.

Four elements - $\left\{a,b,c,d\right\},\left\{a,b,c,e\right\},\left\{a,b,d,e\right\},\left\{a,c,d,e\right\},\left\{b,c,d,e\right\}$.

Five elements - $\left\{a,b,c,d,e\right\}$.

Hence the subsets are,

$\varphi$, $\left\{a\right\},\left\{b\right\},\left\{c\right\},\{d,\left\{e\right\}$, $\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{a,e\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{b,e\right\},\left\{c,d\right\},\left\{c,e\right\},\left\{d,e\right\}$, $\left\{a,b,c\right\},\left\{a,b,d\right\},\left\{a,b,e\right\},\left\{a,c,d\right\},\left\{a,c,e\right\},\left\{a,d,e\right\},\left\{b,c,d\right\},\left\{b,c,e\right\},\left\{b,d,e\right\},\left\{c,d,e\right\}$, $\left\{a,b,c,d\right\},\left\{a,b,c,e\right\},\left\{a,b,d,e\right\},\left\{a,c,d,e\right\},\left\{b,c,d,e\right\}$, $\left\{a,b,c,d,e\right\}$