in the venn diagram, consider u = {whole numb...
in the venn diagram, consider u = {whole numbers 1 - 100}. let a represent numbers that are perfect squares, b represent numbers that are perfect cubes, and c represent numbers that are perfect fourths, or numbers with a fourth root that is an integer. which number(s) satisfy a ∩ c? 16, 81; 1, 16, 81; 1, 4, 9, 16, 25, 36, 49, 81, 100; 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Answer
# Explanation:
## Step1: Identify the elements of set A.
Set A consists of perfect squares between 1 and 100.
$1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100$.
So, $A = \{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\}$.
## Step2: Identify the elements of set C.
Set C consists of perfect fourths between 1 and 100.
$1^4=1, 2^4=16, 3^4=81$. $4^4=256$, which is greater than 100.
So, $C = \{1, 16, 81\}$.
## Step3: Find the intersection of A and C ($A \cap C$).
The intersection $A \cap C$ contains elements that are in both set A and set C.
Comparing the elements of A and C:
$A = \{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\}$
$C = \{1, 16, 81\}$
The common elements are 1, 16, and 81.
$A \cap C = \{1, 16, 81\}$.
# Answer:
O 1, 16, 81