Ina claims that she has proved -2=2. Here proof is shown below.

Question

Ina claims that she has proved -2=2. Here proof is shown below.

Step 1) Assume that -2 = 2.
Step 2) Then square both sides: (-2)2 = (2)2
Step 3) This creates a true statement: 4 = 4
Step 4) This means the assumption that -2 = 2 is correct.
- Identify the errors you see in Ina's proof.

In two sentence

Answer 1

The error in Ina's proof is that she starts with an incorrect assumption that -2 equals 2. Additionally, squaring both sides of an equation does not necessarily preserve the truth of the statement, so Step 3 is invalid.

Answer 2

Ina claims that she has proved -2=2. Here proof is shown below.

Step 1) Assume that -2 = 2.
Step 2) Then square both sides: (-2)2 = (2)2
Step 3) This creates a true statement: 4 = 4
Step 4) This means the assumption that -2 = 2 is correct.
- Classify the type of invalid reasoning that is present in Ina's proof.

In two sentence

Answer 3

The type of invalid reasoning present in Ina's proof is called affirming the consequent. In this case, affirming the consequent occurs when Ina assumes that because a true statement (4 = 4) follows from her assumption, the assumption itself must be true.

Answer 4

The error in Ina's proof is in Step 2, where she squares both sides. Squaring a negative number results in a positive number, so (-2)^2 does not equal (2)^2. Therefore, Step 3 does not create a true statement, and the assumption that -2 = 2 is incorrect.