What is an empty set? How do you find the solution of an empty set?

Question

I was given these equations and told to find the solution of the empty set: 

 

x > -8 and y ≤ x
y < -x and x ≤ 0

y < 2 and x > 2
x + 1 < y and x ≥ y

Answer 1

There may be solutions to equations and inequalities.  However, if a particular equation or inequality has no solution, then we say the solution to the EQUATION or INEQUALITY is the empty set.  Look at the last item in the list, and see that you cannot simultaneously satisfy

 

x + 1 < y and x ≥ y.

 

The set of ordered pairs (x,y) that simultaneously satisfy both inequalities is the empty set, since there is no solution.