FOR THE STUDENT OF MATHEMATICS
DEMONSTRATION CLUB FILE XXII


PURPOSE: To demonstrate that for real number x, real number y and real number z:

                    XXII.     If x = y then x - z = y - z.

is true.



DEMONSTRATION:     STATEMENTS                                       REASONS



                            1.     x - z = x - z                     1.     Property XII   Reflexive:   p = p

                            2.     x = y                               2.     Given ( from the hypothesis or "If" part of the statement. )

                            3.     x - z = y - z                     3.     Property XVIII   Substitution of y for x



Subtraction of the same quantity from both sides of an equality results in an equality.

Can you find another demonstration for this property based on Property XX and Definition 1. for Subtraction?




Would you like to demonstrate Property XXIII. ?

Properties:     List #1 Link     List #2 Link     List #3 Link     List #4 Link     List #5 Link   and   Demonstrations

Copyright © 2009 with all rights reserved by William V. Thayer         Assisted by Peter Rankin, Demo Club Member