A palindromic number is a natural number whose value does not change if its digits are reversed. Examples of palindromic numbers are 11,454 , and 261162 . Use this definition to place 7227 in the correct region of the Venn diagram, where $U$ is the set of natural numbers, $A$ is the set of palindromic numbers, and $B$ is the set of even numbers.
Which of the following regions of the Venn diagram does 7227 belong to?
Answer
Final Answer: \(\boxed{7227} \) belongs to the region of the Venn diagram that represents the set of palindromic numbers but not the set of even numbers. In other words, 7227 belongs to \(A \cap B^c\).
Step 1 ：First, we need to check if 7227 is a palindromic number. A number is palindromic if it remains the same when its digits are reversed. We can do this by converting the number to a string, reversing the string, and checking if the reversed string is equal to the original string.
Step 2 ：Second, we need to check if 7227 is an even number. A number is even if it is divisible by 2. We can do this by checking if the remainder when the number is divided by 2 is 0.
Step 3 ：7227 is a palindromic number but not an even number.
Step 4 ：Final Answer: \(\boxed{7227} \) belongs to the region of the Venn diagram that represents the set of palindromic numbers but not the set of even numbers. In other words, 7227 belongs to \(A \cap B^c\).
