Chapter 13.1, Problem 9AYU

To determine

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

Answer to Problem 9AYU

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

Explanation of Solution

Given:

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

The subsets are,

Zero element - $\varphi$.

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

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

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

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