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Friday, June 14, 2013

MATLAB Commands for Set Operations

SET_THEORY is a MATLAB library which demonstrates how set-theoretic operations can be carried out, primarily using built-in MATLAB commands.
We assume that a set is represented by a strictly ascending sequence of positive integers. We might think of a universal set U = 1 : N in cases where all our subsets will have elements between 1 and N.
Set theoretic operations include
  • definition using a numeric property: A = find ( mod ( U, 3 ) = 1 );
  • definition using an explicit list: A = [ 1, 3, 8];
  • unique: creating a set from the unique elements of a list: A = unique ( [ 1, 3, 8, 3, 3, 1, 7, 3, 1, 1 ] );
  • union: C = union ( A, B );
  • intersection: C = intersect ( A, B );
  • symmetric difference: C = setxor ( A, B );
  • complement with respect to the universal set: B = setdiff ( U, A );
  • complement with respect to another set: C = setdiff ( B, A );
  • cardinality: n = length ( A );
  • membership: true/false = ismember ( a, A );
  • subset: true/false = ismember ( B, A );
  • addition of one element: A = unique ( [ A; a ] );
  • deletion of one element: A = setxor ( A, a );
  • indexing one element: i = find ( A == a );