Chapter 14, Problem 1RE

To determine

The subsets of $\left\{\text{Dave, Joanne, Erica}\right\}$.

Answer to Problem 1RE

The subsets of $\left\{\text{Dave, Joanne, Erica}\right\}$ are,

$\left\{\text{Dave}\right\},\left\{\text{ Joanne}\right\},\left\{\text{Erica}\right\},\left\{\text{Dave, Joanne}\right\},\left\{\text{Dave},\text{Erica}\right\},\left\{\text{Joanne, Erica}\right\},\left\{\text{Dave, Joanne, Erica}\right\}$

Explanation of Solution

Given:

The set is defined as $\left\{\text{Dave, Joanne, Erica}\right\}$.

Definition used:

Subset:

When a set of elements are contained in another set then it is termed as subset, it is denoted by the symbol $\subseteq$. In other words, consider set A and B, if all the elements of set A are contained in set B then A is subset of B, that is $A\subseteq B$.

Calculation:

Consider the set $\left\{\text{Dave, Joanne, Erica}\right\}$.

The set that contains no elements is an empty set $\{\varnothing \}$. This is subset of every set.

The subsets with one element is $\left\{\text{Dave}\right\},\left\{\text{ Joanne}\right\},\left\{\text{Erica}\right\}$

The subsets with two elements is $\left\{\text{Dave, Joanne}\right\},\left\{\text{Dave},\text{Erica}\right\},\left\{\text{Joanne, Erica}\right\}$.

The subset with three elements is $\left\{\text{Dave, Joanne, Erica}\right\}$.

Thus, the subsets of set $\left\{\text{Dave, Joanne, Erica}\right\}$ are,

$\left\{\text{Dave}\right\},\left\{\text{ Joanne}\right\},\left\{\text{Erica}\right\},\left\{\text{Dave, Joanne}\right\},\left\{\text{Dave},\text{Erica}\right\},\left\{\text{Joanne, Erica}\right\},\left\{\text{Dave, Joanne, Erica}\right\}$