Sets and Functions (VIII): The difference between two sets A and B, denoted by A – B, is the set of all elements in A and not in B, thus A – B = A∩B’. Show that (AUB) – C = (A – C)U(B – C).

Topology Sets and Functions (VIII) The Algebra of Sets The difference between two sets A and B, denoted by A – B, is the set of all elements in A and not in B, thus A – B = A∩B’. Show that (AUB) – C = (A – C)U(B – C).

Sets and Functions (IX): The difference between two sets A and B, denoted by A – B, is the set of all elements in A and not in B, thus A – B = A∩B’. Show that A – (BUC) = (A – B)∩(A – C).

Topology Sets and Functions (IX) The Algebra of Sets The difference between two sets A and B, denoted by A – B, is the set of all elements in A and not in B, thus A – B = A∩B’. Show that A – (BUC) = (A – B)∩(A – C).

Sets and Functions (X): 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 Δ ( B Δ C ) = ( A Δ B ) Δ C.

Topology Sets and Functions (X) The Algebra of Sets The Symmetric Difference of two Sets 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 Δ ( B Δ C ) = ( A Δ B ) Δ C.

Sets and Functions (XI): 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 Δ φ = A ; A Δ A = φ.

Topology Sets and Functions (XI) 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 Δ φ = A ; A Δ A = φ

Sets and Functions (XI): 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 Δ B = B Δ A .

Topology Sets and Functions (XII) 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 Δ B = B Δ A .