1. Identify the error in Mani's proof that 2 = 1. Justify your reasoning.

Let x and y be equal qualities

step 1 : x = y

step 2 : x^2 (squared) = xy

step 3 : x^2 - y^2 = xy - y^2

step 4 : ( x -y )( x + y ) = y( x - y)

step 5 : x + y = y

step 6 : y + y = y

step 7 : 2y = y

step 8 : 2 = 1

2. Consider the following arguments. For each argument, decide whether the argument is valid or invalid. Justify your reasoning. You may use Venn diagrams to support your solution. (Note: Attach your completed Venn diagrams to the Lesson 4 Assignment.)

x2 a. Some solutions to the equations are integers. Some integers are greater than zero. Therefore, some solutions to the equations are greater than zero.

b. If Isabelle washes her mom's car, she will be paid $5.00 per hour. Isabelle washes her mom's car for 2 h, so she gets paid $10.00.