Question

Given sets X and Y , we define the symmetric (set) difference of X and Y (notation: X4Y ) to be the set X4Y := (X ∪ Y ) \ (X ∩ Y ). Do the following

Answer 1

Here are some properties of the symmetric difference that will help you.

Explanation:

We define the symmetric (set) difference of X and Y (notation: XΔY ) to be the set XΔY := (X ∪ Y ) \ (X ∩ Y ).

Example:

{1,2,3}Δ{3,4}={1,2,4}

The symmetric difference is commutative:

XΔY=YΔX

The symmetric difference is associative:

XΔ(YΔZ)=(XΔY)ΔZ

Also:

XΔ∅=X

XΔX=∅

Intersection distributes over symmetric difference:

X∩(YΔZ)=(X∩Y)Δ(X∩Z)