Answered

Answer true or false for the following statement:

[tex]\[{x \mid x \text{ is a whole number greater than 9 and less than 12}} = \{10, 11\}\][/tex]

Choose the correct answer below.

A. The statement is true. The whole numbers 10 and 11 are the only members in the set of whole numbers greater than 9 and less than 12.
B. The statement is false. The whole numbers 10 and 11 are not the only members. The set should include all whole numbers between 9 and 12.
C. The statement is true. The whole numbers 10 and 11 are the only whole numbers greater than 9 and less than 12.
D. The statement is false. The list of whole numbers is incomplete. There are other whole numbers between 9 and 12.



Answer :

GinnyAnswer
The question asks whether the set of whole numbers greater than 9 and less than 12 is the same as the set {10, 1.1}.

First, let's define the set of whole numbers greater than 9 and less than 12. Whole numbers are non-negative integers (0, 1, 2, 3, ...). The whole numbers greater than 9 and less than 12 are:
- 10
- 11

Therefore, the set of whole numbers greater than 9 and less than 12 is {10, 11}.

Next, let's examine the given set, which is {10, 1.1}.

- 10 is a whole number.
- 1.1 is not a whole number; it is a decimal or a real number.

Now, we can compare the two sets:
- {10, 11}
- {10, 1.1}

Clearly, these two sets are not the same, because 11 is not present in the second set and 1.1 is not present in the first set. Therefore, the statement "{x x is a whole number greater than 9 and less than 12}={10,1.1}" is false.

So, the correct answer is:
OD. The statement is false. The list of whole numbers is incomplete. There are other whole numbers between 9 and 12