Question

if a=b then x+a=x+b
(converse of cancellation law) ​

Answer 1

The definition of converse of cancellation law is given as

In an algebraic structure A  with a binary operation,

So that the cancellation laws for left and right respectively hold it for all

$X,Y,Z \\ XY=XZ \\ Y=Z,\\ X.Y=Z.Y\\ X=Z$

Such type of structure is nothing but the cancellative.

Now in the above question

Their is cancellation for addition.

As we know

When

$a=b, then \\ x+a=x+b$

So by using cancellation property for addition we get

$a+x\leq b+x,then\\ a\leq b$