Question

determine whether the following statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. the set of subsets of {9, 19} contains 8 elements. choose the correct answer below. a. the statement is true. b. the statement should be changed to \the set of subsets of {9, 19} contains 2 elements.\ c. the statement should be changed to \the set of subsets of {9, 19} contains 4 elements.\

Explanation:

Step1: Recall subset count formula

For a set with $n$ elements, number of subsets is $2^n$.

Step2: Identify $n$ for given set

The set $\{9, 19\}$ has $n=2$ elements.

Step3: Calculate total subsets

$2^2 = 4$

Step4: Evaluate the statement

The original statement claims 8 elements, which is false. The correct number is 4.

Answer:

C. The statement should be changed to "The set of subsets of {9, 19} contains 4 elements."