Sets and Functions (XIII): The symmetric difference of two sets A and B, denoted by A Δ B, is defined by A Δ B = ( A – B ) U ( B – A ); it is thus the union of their differences in opposite orders. Show that A ∩ (B Δ C) = (A ∩ B) Δ (A ∩ C) .

Topology Sets and Functions (XIII) The Algebra of Sets The Symmetric Difference of two Sets The symmetric difference of two sets and , denoted by , is defined by ; it is thus the union of their differences in opposite orders. Show that A ∩ (B Δ C) = (A ∩ B) Δ (A ∩ C).

The Symmetric Difference of two Sets: A ring of sets is a non-empty class A of sets such that if A and B are in A, then A Δ B and A ∩B are also in A. Show that A must also contain the empty set.

Topology Sets and Functions (XIV) The Algebra of Sets Ring of Sets The Symmetric Difference of two Sets A ring of sets is a non-empty class A of sets such that if A and B are in A, then A Δ B and A ∩B are also in A. Show that A must also contain the empty set.

The Symmetric Difference of two Sets: A ring of sets is a non-empty class A of sets such that if A and B are in A, then A Δ B and A∩B are also in A. Show that A must also contain the A - B.

Topology Sets and Functions (XV) The Algebra of Sets Ring of Sets The Symmetric Difference of two Sets A ring of sets is a non-empty class A of sets such that if A and B are in A, then A Δ B and A∩B are also in A. Show that A must also contain the A - B.

The Symmetric Difference of two Sets: A ring of sets is a non-empty class A of sets such that if A and B are in A, then A Δ B and A∩B are also in A. Show that A must also contain the AUB.

A ring of sets is a non-empty class A of sets such that if A and B are in A, then A Δ B and A∩B are also in A. Show that A must also contain the AUB.

Sets and Functions (XVII): Show that if a non-empty class of sets contains the union and difference of any pair of its sets, then it is a ring of sets.

Show that if a non-empty class of sets contains the union and difference of any pair of its sets, then it is a ring of sets.