Algebraic Symmetry Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Is f(x,y)=xโˆ’yf(x, y) = x - y symmetric?

Solution

  1. 1
    f(y,x)=yโˆ’x=โˆ’(xโˆ’y)โ‰ xโˆ’yf(y, x) = y - x = -(x - y) \neq x - y (unless x=yx = y).
  2. 2
    Not symmetric. It is anti-symmetric: f(y,x)=โˆ’f(x,y)f(y,x) = -f(x,y).

Answer

No, it is anti-symmetric.
The expression xโˆ’yx - y changes sign when xx and yy are swapped. Anti-symmetric expressions satisfy f(y,x)=โˆ’f(x,y)f(y, x) = -f(x, y), a different type of symmetry.

About Algebraic Symmetry

The property of an expression or equation that remains unchanged when certain transformations โ€” such as swapping variables โ€” are applied.

Learn more about Algebraic Symmetry โ†’

More Algebraic Symmetry Examples

Example 1 easy

Is [formula] symmetric in [formula] and [formula]?

Example 2 medium

Is [formula] symmetric?

Example 4 medium

If [formula] and [formula], find [formula].

โ† All Algebraic Symmetry Examples Algebraic Symmetry Concept