Question

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

Short answer

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

Step-by-step solution

Step 1. Given Information.

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

Step 2. Subsets.

The total number of subsets are $2^n$where $n=4$.

So, number of subsets are $2^4=16$.

0 elements - $\varnothing$.

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

2 elements - localid="1646976761171" $\left\{a,b\right\},\left\{a,c\right\},\left\{a,d\right\},\left\{b,c\right\},\left\{b,d\right\},\left\{c,d\right\}$.

3 elements - localid="1646976797520" $\left\{a,b,c\right\},\left\{a,c,d\right\},\left\{a,b,d\right\},\left\{b,c,d\right\}$.

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