Question

Use complete sentences to describe why SetA=x∣x is an even whole number between 0 and 2=0.

Answer 1

SetA = {0}. SetA is defined as the set of even whole numbers between 0 and 2, and in this case, the only number that satisfies this criteria is 0

Step-by-step explanation:

SetA is defined as the set of even whole numbers between 0 and 2. In this case, the only even whole number within this range is 0. Therefore, SetA is a singleton set containing only the element 0.

In mathematical terms, an even number is one that is divisible by 2 without leaving a remainder. The only even whole number between 0 and 2 is 0 itself. The set notation x can be expressed as {0}, indicating that the set contains only the element 0.

This result aligns with the definition of even numbers and the specified range, providing a concise and accurate answer to the question. Therefore, SetA is indeed equal to {0}.

To further illustrate, consider the integers within the given range: 0, 1, and 2. 0 is the only even number, as it can be expressed as 2 multiplied by 0. Numbers 1 and 2, being odd and even, respectively, are not part of SetA. Therefore, the set is simply {0}, capturing the essence of even whole numbers between 0 and 2 and providing a clear and succinct representation of SetA.

Answer 2

Set
`\(A = \{x \mid x \text{ is an even whole number between } 0 \text{ and } 2\}\)` is equal to
`\(A = \{0, 2\}\).`

Step-by-step explanation:

In the given set (A), we are looking for even whole numbers between 0 and 2. The even numbers in this range are 0 and 2. Therefore, (A) can be expressed as (A = {0, 2}).

Now, let's break down the explanation further:

1. Inclusion of 0: The set includes 0 because 0 is an even number. An even number is any integer that is exactly divisible by 2, and 0 meets this criterion.

2. Inclusion of 2: Similarly, 2 is included in the set because it is also an even number. Being divisible by 2, it satisfies the condition of being an even whole number between 0 and 2.

3. Exclusion of Other Numbers: Since the set is specified to contain only even whole numbers, any odd number or fraction is excluded. In this case, only 0 and 2 fit the criteria, resulting in the final set (A = {0, 2}).