Sets and Functions : True Subsets
Let U be the set { 1, 2, 3}. There are 8 subsets . What are they? If A and B are arbitrary subsets of U, there are 64 possible relations of the form “A is subset of B”. Count the number of true ones.
Topology Sets and Functions (IV) The Algebra of Sets If { Ai } and { Bj } are two classes of sets such that { Ai } is subset of { Bj }, show that Ui Ai is subset Uj Bj and ∩j Bj is subset of ...continues
Sets and Functions : Set Difference
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 – B = A – (A∩B) = (A U B) – B .
Sets and Functions : Set Difference
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 – B) – C = A – (BUC).
Sets and Functions : Set Difference
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 – (B – C) = (A – B)U(A∩C).
Sets and Functions : Set Difference
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 : Set Difference
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 : 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 : 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 : 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 .
