Given the statement "the quotient of two integers is an integer", we could determine if it is true or false.
Let us consider two integers, say A and B. If the A divides B and the result (i.e. the quotient) divides evenly then, the statement is true. If A is 4 and B is 2, the quotient is as shown below
[tex]\frac{A}{B}=\frac{4}{2}=2[/tex]From the above example, the quotient is an integer
If A is 2 and B is 4, the quotient is as shown below
[tex]\frac{A}{B}=\frac{2}{4}=\frac{1}{2}[/tex]From the above example, the quotient is a fraction and not an integer.
Hence, the statement "the quotient of two integers is an integer" is FALSE based on the above examples.
