Question

The set of integers is closed under the operation of addition.

A: Which equation illustrates this concept?


B: Which statement correctly explains this concept?


Select one answer for question A and one answer for question B.


A: 2+27=29

A: 34÷4=172

A: 1−3=−2

A: 2⋅6=12

B: The sum of the integers 2 and 27 is the integer 29, which demonstrates that integers are closed under addition.

B: The quotient of the integers 34 and 4 is the integer 172, which demonstrates that integers are closed under addition.

B: The difference of the integers 1 and 3 is not an integer, −2, which does not demonstrate that integers are closed under addition.

B: The product of the integers 2 and 6 is not an integer, 12, which does not demonstrate that integers are closed under addition.

Answer 1

A: 2+27=29

B: The sum of the integers 2 and 27 is the integer 29, which demonstrates that integers are closed under addition.

Explanation:

Since, closed property of addition for a set A is defined as,

∀ x, y ∈ A ⇒ x + y ∈ A,

∵ Set of integer is closed under multiplication,

If Z represents the set of integer,

Then 2, 27 ∈ Z ⇒ 2 + 27 = 29 ∈ Z,

Hence, the equation illustrates given statement,

2+27 = 29

The statement that correctly explains given statement,

The sum of the integers 2 and 27 is the integer 29, which demonstrates that integers are closed under addition.c