Question

Given mA+ mB=mB + mC prove mC= mA Write a paragraph proof to prove the statement

Answer 1

Answer: So, you can subtract  m_B  from both sides to transform the equality into

m_A+ m_B=m_B + m_C \to m_A+ m_B-m_B=m_B + m_C-m_B \to m_A=m_C  

as required.

Step-by-step explanation:

Answer 2

As a property of equations, you can add or subtract the same quantity to/from both sides, and the truth value of the equality will remain the same: if you start with something true, e.g. 7=7 and add the same quantity to both sides, e.g. 7+4=7+4, you will still have something true, i.e. 11=11.

On the other hand, if you start with something false, e.g. 3=7 and add the same quantity to both sides, e.g. 3+6=7+6, you will still have something false, i.e. 9=13.

So, you can subtract $m_B$ from both sides to transform the equality into

$m_A+ m_B=m_B + m_C \to m_A+ m_B-m_B=m_B + m_C-m_B \to m_A=m_C$

as required.