if ab=bc and bc=cd how can I assume that ab=cd?

Question

i want to know the proof of it.

Answer 1

The property is called the Transitive Property.

 

Since ab = bc, ab-bc=0

 

Since bc = cd, bc-cd = 0

 

0 + 0 = 0

 

So, (ab-bc) + (bc-cd) = 0

 

The bc terms cancel out to give ab - cd = 0

 

Adding cd to both sides yields ab = cd