Questions: Let the set A be defined as follows. A=3,34,83,89 (a) Find the total number of proper subsets of A. (b) Find the total number of subsets of A.

Transcript text: Let the $\operatorname{set} A$ be defined as follows. \[ A=\{3,34,83,89\} \] (a) Find the total number of proper subsets of $A$. $\square$ (b) Find the total number of subsets of $A$. $\square$

Solution

Solution Steps

Solution

Given a set $A$ with $n$ elements, where $n$ is 4.

Step 1: Total Number of Subsets of $A$

The total number of subsets of a set with $n$ elements is given by the formula $2^n$. Substituting the given value of $n$ into the formula, we get $2^{4} = 16$.

Step 2: Total Number of Proper Subsets of $A$

The total number of proper subsets of a set with $n$ elements is given by the formula $2^n - 1$. Using the value of $n$ provided, we calculate $2^{4} - 1 = 15$.