Answer:
yes
yes
yes
sometimes
closure property of integer under the 4 operations
Explanation:
I think this is the question:
If x is an integer is 2x an integer?
Is x + 2 an integer?
Is x − 2 an integer?
Is x ÷ 2 an integer?
What property does this illustrate?
Answer:
If x is an integer is 2x an integer? Yes
If x is an integer, then 2x is an integer. 2 is an integer. Multiplying an integer by another integer always results in an integer.
Is x + 2 an integer? Yes
The sum of two integers is always an integer.
Is x − 2 an integer? Yes
The difference of two integers is always an integer.
Is x ÷ 2 an integer? Yes for some values of x, but not for all values of x.
The property these questions illustrate is the closure property.
The closure property applies to addition, subtraction, and multiplication of integers. That means that if you add two integers, find the difference between two integers, or multiply two integers, the answer is an integer.
There is no closure property of integers under division because when you divide an integer by another integer, you do not always get an integer quotient.