1. consider the operation * defined by x* y = x + lyl.
which of the following sets are closed under this operation?
- integers
negative integers
positive integers
integer multiples of 3

Integers are closed:

If y is an integer, so is its absolute value |y|. So, x + |y| is a sum between two integers (it's either x + y or x - y, depending on the sign of y), and the sum between two integers is an integer.

Negative integers are not closed:

If you pick x and y such that , you'll get a counterexample.

For example, if we choose we have

which is positive. So, we started with two negative numbers and we got a positive number, which means that negative numbers are not closed under this operator.

Positive integers are closed:

If x and y are both positive, then the absolute value is useless, because |y| = y. So, we have

And our operator * is the usual sum. And the sum of two positive numbers is a positive number, so positive numbers are closed.

Multiples of 3 are closed.

If x and y are multiple of 3, then there exist integers m and n such that

This implies that

which is a multiple of 3, because we wrote it as "3 times something".

So, if we start with two multiples of 3 we get another multiple of 3, which means that multiples of 3 are closed.

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.

answer: the answer is one

step-by-step explanation:

pemdas, in this situation there is no parenthesis or exponents so you go to multiplication, 1x1=1, then division 1/1= 1 then addition 1+1=2 then subtraction 2-1=1