Question

Verify that the set of integers $Z$ is closed under addition and multiplication. Also check if $Z$ is closed under subtraction and division.

Answer 1

Step 1 : Integers ($Z$) are closed under addition and multiplication.

For addition $2+3=5$

For multiplication $2\times 3=6$

Step :2 Integers are not closed under subtraction and division.

For subtraction $2-3=-1$

For division $2÷3=\frac{2}{3}$, here $\frac{2}{3}$ is not an integer.

Hence, the set of integers $Z$ is closed under addition, subtraction and multiplication but does not close under division.