Questions: Let the set A be defined as follows. A=3,13,17,19,29,31,53 (a) Find the total number of subsets of A. (b) Find the total number of proper subsets of A.

Transcript text: Let the set $A$ be defined as follows. \[ A=\{3,13,17,19,29,31,53\} \] (a) Find the total number of subsets of $A$. $\square$ (b) Find the total number of proper subsets of $A$. $\square$

Solution

Solution Steps

Solution

Given a set $A$ with $n$ elements, where $n$ is 7.

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 $2^{7} = 128$.

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 $2^{7} - 1 = 127$.