Write a C++ program and algorithms for above mentioned all set operations

. Design algorithms for following set operations on sets A and B Check whether A satifies definition of set Find cardinality of A Element a belongs to A Complement of A considering A is a subset of universal set U Union of A and B Intersection of A and B Set difference A - B Check whether A is a subset of B Check whether A is a superset of B O Cartesian Product - Ax B Power set of A - P(A) . Provide time and space required by each of the algorithms . Prove that the algorithms are correct . Considering U={a,...,Z}, A={a,f,1,q} and B={d,f,m,w} give trace for each algorithms