Are the rational numbers closed under multiplication?

Yes, The rational numbers are closed under multiplication.

Step-by-step explanation:

A rational number is a number which can be expressed in the form of a fraction , where x and y are integers and y ≠ 0.

Now, closure property of multiplication states that if two rational numbers are multiplied then the product is also a rational number. Thus, if r and t are rational numbers, then

r×t = s, where s is the product of r and t

s is also a rational number.

Hence, the rational numbers are closed under multiplication.

This can be better explained with the help of an example ,

It is clear that is a rational number.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c