Properties of Addition and Subtraction of Integers

Which of the following is true?

Integers are not associative under: 

Integers are not commutative under: 

The sum of  $-7$ and $3$ is  

The closure property says,

Take two integers $4,6$ and show that the difference of any two integers will always be an integer.

Explain with an example, that the difference of any two integers will always be an integer.

Select the appropriate sign$\left(=,\ne \right)$  for the given statement,

 $5-\left(3-2\right),\left(5-3\right)-2$

Sum of given integer show closure property.

$5,2,8,6,10,12$.               [Enter true/false]

Does $7+2=9$, show closure property.

Examples and some properties of integers are given below. Match the correct property and its example.

                      Example                                  Property

$$\begin{gathered} \left(\mathrm{i}\right) (a+b)+c=a+(b+c) \left(\mathrm{a}\right)\mathrm{Identity} \\ \left(\mathrm{ii}\right) 3+4=4+3 \left(\mathrm{b}\right)\mathrm{Associativity} \\ \left(\mathrm{iii}\right) (-4)+0=(-4) \left(\mathrm{c}\right)\mathrm{Commutativity} \end{gathered}$$

$17+$ _____ $=17$

In the following question, the number in the central block is related to any number from the numbers on the sides of the panel. Find the number in place of question mark (?).

(a)

(b)

(c)

Which of the following expression are equal to $-20 ?$
$$\begin{gathered} \mathrm{I} -4 \times 5 \\ \mathrm{II} -32+ 10 -(-2) \\ \mathrm{III} -6\times 2 - [-2\times 4] \\ \mathrm{IV} 5\times (-2)+(-3)\times 4 \end{gathered}$$

Is subtraction of integers commutative? Give an example to support your answer.