Suggested languages for you:

Americas

Europe

Q 10.

Expert-verified
Found in: Page 847

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Write down all the subsets of $\left\{a,b,c,d,e\right\}$.

The subsets are :$\varnothing ,\left\{a\right\},\left\{b\right\},\left\{c\right\},\left\{d\right\},\left\{e\right\},\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{a,e\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{b,e\right\},\left\{c,d\right\},\left\{c,e\right\},\left\{d,e\right\},\left\{a,b,c\right\},\left\{a,b,d\right\},\left\{a,b,e\right\},\left\{a,c,d\right\},\left\{a,c,e\right\},\left\{a,d,e\right\},\left\{b,c,d\right\},\left\{b,c,e\right\},\left\{b,d,e\right\},\left\{c,d,e\right\},\left\{c,d,a\right\},\left\{a,b,c,d\right\},\left\{a,b,c,e\right\},\left\{a,b,d,e\right\},\left\{a,c,d,e\right\},\left\{b,c,d,e\right\},\left\{a,b,c,d,e\right\}$

See the step by step solution

## Step 1. Given Information.

Write down all the subsets of $\left\{a,b,c,d,e\right\}$.

## Step 2. Subsets.

The total number of subsets are ${2}^{n}$ where $n=5$.

The number of subsets are ${2}^{5}=32$.

The 0 elements - $\varnothing$.

The 1 elements - $\left\{a\right\},\left\{b\right\},\left\{c\right\},\left\{d\right\},\left\{e\right\}$.

The 2 elements - role="math" $\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{a,e\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{b,e\right\},\left\{c,d\right\},\left\{c,e\right\},\left\{d,e\right\}$.

The 3 elements - $\left\{a,b,c\right\},\left\{a,b,d\right\},\left\{a,b,e\right\},\left\{a,c,d\right\},\left\{a,c,e\right\},\left\{a,d,e\right\},\left\{b,c,d\right\},\left\{b,c,e\right\},\left\{b,d,e\right\},\left\{c,d,e\right\},\left\{c,d,a\right\}$.

The 4 elements - $\left\{a,b,c,d\right\},\left\{a,b,c,e\right\},\left\{a,b,d,e\right\},\left\{a,c,d,e\right\},\left\{b,c,d,e\right\}$.

The 5 elements - $\left\{a,b,c,d,e\right\}$.