Question

With respect to which of the following operations, is closure property satisfied by the set of integers?
Addition, Multiplication
Addition, Division, Multiplication
Addition, Multiplication, Subtraction
Addition, Subtraction, Division

Answer 1

Answer:

Closure property holds for the addition, subtraction and multiplication of integers

Step-by-step explanation:

Closure property of integers under addition:

The sum of any two integers will always be an integer, i.e. if a and b are any two integers, a + b will be an integer.

Example: (-8) + 6 = 2

11 + 9 = 20

Closure property of integers under subtraction:

The difference between any two integers will always be an integer, i.e. if a and b are any two integers, a – b will be an integer.

Example: 19 – 6 = 13

-6 – (-3) = -3

Closure property of integers under multiplication:

Any two integers’ product will be an integer, i.e. if a and b are any two integers, ab will also be an integer.

Example: 3 × (-9) = -27

(–7) × (-9) = 63

Closure property of integers under division:

Division of integers doesn’t follow the closure property since the quotient of any two integers a and b, may or may not be an integer. Sometimes the quotient is undefined (when the divisor is 0).

Example: -16 ÷ 4 = -4 (an integer)

(−4) ÷ (−16) = 1/4 (not an integer)