Question

From inside Room I, Bill overheard the following conversation between a group of humans (from Earth 1), who gathered near a job fair in the premises of “The Hall of Operations”, with a banner which read “Vacancies open for numbers which are closed under addition”:

Supriya (looking at the banner): What does “closed” in the banner mean?

Ajit (with a poker face): If a set of numbers is closed for a particular operation, then it is said to possess the closure property under that operation.

Supriya (unimpressed): That’s just a textbook definition. I want to understand what that actually means.

Arjun: Supriya, a set of numbers is said to be closed under a particular mathematical operation when the result of that operation also belongs to the same set of numbers.

Supriya then made 4 statements, each of which is presented in the following options. Chose the correct options made by Supriya. She might make more than one correct statement.

• A. Addition of two integers always results in an integer
• B. Subtraction of two integers need not necessarily result in an integer
• C. Multiplication of two integers always results in an integer
• D. Division of two integers need not necessarily result in an integer

Answer 1

Answer: (A), (C), (D)

The correct options are
A

Addition of two integers always results in an integer

C

Multiplication of two integers always results in an integer

D

Division of two integers need not necessarily result in an integer

Integers are closed for addition, subtraction and multiplication but not for division.
For eg, -1 + 10 = 9
-2 - (-3) = 1
2 x (-6) = (-12)
as can be seen, the result is also an integer. But, the result of division of two integers may not be an integer. For eg,
$2÷6=2/6$
here, the result, 2/6, is not an integer.