Question

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

Short answer

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

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